Categories of Bid`ah and Shirk
Question

Can we call people who do Shirk and Bid`ah Muslims?
Praise be to Allah.This question involves two issues, Bid`ah (innovation) and Shirk (polytheism, association of others with Allah). 

Bid`ah

This issue may be divided into three topics:

Definition of Bid`ah
Categories of Bid`ah
Rulings on one who commits Bid`ah – does that make him a disbeliever or not? 

What is Bid`ah?
Shaykh Muhammad ibn `Uthaymin (may Allah have mercy on him) said: 
“According to Shari`ah, the definition of Bid`ah is `Worshipping Allah in ways that Allah has not prescribed.’ If you wish you may say, `Worshipping Allah in ways that are not those of the Prophet (peace and blessings of Allah be upon him) or his rightly guided Caliphs.’” 
The first definition is taken from the verse (interpretation of the meaning):
“Or have they partners with Allah (false gods) who have instituted for them a religion which Allah has not ordained?”  [Ash-Shura 42:21] 
The second definition is taken from the Hadith of the Prophet (peace and blessings of Allah be upon him), who said:
“I urge you to adhere to my way (Sunnah) and the way of the rightly-guided Caliphs who come after me. Hold fast to it and bite onto it with your eyeteeth [i.e., cling firmly to it], and beware of newly-invented matters.” 
So everyone who worships Allah in a manner that Allah has not prescribed or in a manner that is not in accordance with the way of the Prophet (peace and blessings of Allah be upon him) or his rightly-guided Caliphs, is an innovator, whether that innovated worship has to do with the names and attributes of Allah, or to do with His rulings and laws. 
With regard to ordinary matters of habit and custom, these are not called Bid`ah (innovation) in Islam, even though they may be described as such in linguistic terms. But they are not innovations in the religious sense, and these are not the things that the Prophet (peace and blessings of Allah be upon him) was warning us against. 
And there is no such thing in Islam as Bid`ah hasanah (good innovation).” (Majmu` Fatawa Ibn `Uthaymin, vol. 2, p. 291) 
Categories of Bid`ah 
Bid`ah may be divided into two categories: 

Bid`ah which constitutes disbelief  
Bid`ah which does not constitute disbelief 

Bid`ah which constitutes disbelief 
 If you ask, what is the definition of Bid`ah which constitutes disbelief and that which does not constitute disbelief? 
The answer is: 
Shaykh Hafith Al-Hakami (may Allah have mercy on him) said: 
“The kind of Bid`ah which constitutes disbelief is when one denies a matter on which there is scholarly consensus, which is widely-known, and which no Muslim can have any excuse for not knowing, such as denying something that is obligatory, making something obligatory that is not obligatory, or making something prohibited permissible, or making something permissible prohibited; or believing some notion about Allah, His Messenger and His Book when they are far above that, whether in terms of denial of affirmation  – because that means disbelieving in the Quran and in the message with which Allah sent His Messenger (peace and blessings of Allah be upon him). 
Examples include the Bid`ah of the Jahmiyyah, who denied the attributes of Allah; or the notion that the Quran was created; or the notion that some of the attributes of Allah were created; or the Bid`ah of the Qadariyyah  who denied the knowledge and actions of Allah; or the Bid`ah of the Mujassimah who likened Allah to His creation… etc. 
Bid`ah which does not constitute disbelief 
The second category, Bid`ah which does not constitute disbelief, is defined as that which does not imply rejection of the Quran or of anything with which Allah sent His messengers. 
Examples include the Marwani Bid`ahs (which were denounced by the greatest Companions (who did not approve of them, although they did not denounce them as disbelievers or refuse to give them Bay`ah because of that), such as delaying some of the prayers until the end of the due times, doing the ‘Eid Khutbah before the ‘Eid prayer, delivering the Khutbah whilst sitting down on Fridays, etc.” (Ma`arij Al-Qubul, 2/503-504) 
Can you call one who commits Bid`ah  a disbeliever? 
The answer is that it depends. 
If the Bid`ah constitutes disbelief, then the person is one of the following two types: 

Either it is known that his intention is to destroy the foundations of Islam and make the Muslims doubt it. Such a person is definitely a disbeliever; indeed, he is a stranger to Islam and is one of the enemies of the faith.
Or he is deceived and confused; he cannot be denounced as a disbeliever until proof is established against him, fair and square. 

If the Bid`ah does not constitute disbelief, then he should not be denounced as a disbeliever. Rather, he remains a Muslim, but he has done a gravely evil action. 
How should we deal with those who commit Bid`ah? 
The answer is: 
Shaykh Muhammad ibn `Uthaymin (may Allah have mercy on him) said: 
“In both cases, we have to call these people – who claim to be Muslim but who commit acts of Bid`ah which may constitute disbelief or may be less than that – to the truth, by explaining the truth without being hostile or condemning what they are doing. But once we know that they are too arrogant to accept the truth – for Allah says (interpretation of the meaning), `And insult not those whom they (disbelievers) worship besides Allah, lest they insult Allah wrongfully without knowledge.’ [Al-An`am 6:108] – if we find out that they are stubborn and arrogant, then we should point out their falsehood, because then pointing out their falsehood becomes an obligation upon us. 
With regard to boycotting them, that depends upon the Bid`ah. If it is a Bid`ah which constitutes disbelief, then it is obligatory to boycott the person who does it. If it is of a lesser degree than that, then it is essential to examine the situation further. If something may be achieved by boycotting the person, then we do it; if no purpose will be served by it, or if it will only make him more disobedient and arrogant, then we should avoid doing that, because whatever serves no purpose, it is better not to do it. And also in principle it is impermissible to boycott a believer, because the Prophet (peace and blessings of Allah be upon him) said: `It is not permissible for a man to forsake [not speak to] his brother for more than three [days].’” (Adapted from Majmu` Fatawa Ibn `Uthaymin, vol. 2, p. 293) 

Shirk, its types and the definition of each 

Types of Shirk
Shaykh Muhammad ibn `Uthaymin (may Allah have mercy on him) said: 
“Shirk is of two types, major Shirk which puts a person beyond the pale of Islam, and minor Shirk .” 

The first type, major Shirk , is “Every type of Shirk which the Lawgiver described as such and which puts a person beyond the pale of his religion” – such as devoting any kind of act of worship which should be for Allah to someone other than Allah, such as praying to anyone other than Allah, fasting for anyone other than Allah or offering a sacrifice to anyone other than Allah. It is also a form of major Shirk to offer supplication (Du`a) to anyone other than Allah, such as calling upon the occupant of a grave or calling upon one who is absent to help one in some way in which no one is able to help except Allah. 
The second type is minor Shirk , which means every kind of speech or action that Islam describes as Shirk, but it does not put a person beyond the pale of Islam – such as swearing an oath by something other than Allah, because the Prophet (peace and blessings of Allah be upon him) said that whoever swears an oath by something other than Allah is guilty of disbelief or Shirk .

The one who swears an oath by something other than Allah but does not believe that anyone other than Allah has the same greatness as Allah, is a Mushrik who is guilty of lesser Shirk, regardless of whether the one by whom he swore is venerated by people or not. It is not permissible to swear by the Prophet (peace and blessings of Allah be upon him), or by the president, or by the Ka`bah, or by Jibril, because this is Shirk, but it is minor Shirk which does not put a person beyond the pale of Islam. 
Another type of minor Shirk is showing off, which means that a person does something so that people will see it, not for the sake of Allah. 
Impact of showing off on acts of worship
The ways in which showing off may cancel out acts of worship are either of the following: 

The first is when it is applied to an act of worship from the outset, i.e., the person is not doing that action for any reason other than showing off. In this case, the action is invalid and is rejected, because of the Hadith of Abu Hurayrah (may Allah be pleased with him) which was attributed to the Prophet (peace and blessings of Allah be upon him), which says that Allah said, “I am so Self-sufficient that I am in no need of having an associate. Thus he who does an action for someone else’s sake as well as Mine will have that action renounced by Me to him whom he associated with Me.” (Narrated by Muslim, Kitaab Az-Zuhd, 2985) 
The second is when the showing off happens later on during the act of worship, i.e., the action is originally for Allah, then showing off creeps into it. This may be one of two cases: 

The first is when the person resists it – this does not harm him.
For example, a man has prayed a Rak`ah, then some people come along during his second Rak`ah and it occurs to him to make the Ruku` or Sujud longer, or makes himself weep, and so on. If he resists that, it does not harm him, because he is striving against this idea. But if he goes along with that, then every action which stemmed from showing off is invalid, such as if he made his standing or prostration long, or he made himself weep – all of those actions will be cancelled out. But does this invalidation extend to the entire act of worship or not? 
We say that either of the following must apply: 

Either the end of his act of worship was connected to the beginning (with no pause); so if the end of it is invalidated then all of it is invalidated.

This is the case with the prayer – the last part of it cannot be invalidated without the first part also being invalidated, so the whole prayer is invalid.

Or if the beginning of the action is separate from the end of it, then the first part is valid but the latter part is not. Whatever came before the showing off is valid, and what came after it is not valid. 

An example of that is a man who has a hundred Riyals, and gives fifty of them in charity for the sake of Allah with a sound intention, then he gives fifty in charity for the purpose of showing off. The first fifty are accepted, and the second fifty are not accepted, because the latter is separate from the former.” (Majmu` Fatawa wa Rasa’il Ibn `Uthaymin, and Al-Qawl Al-Mufid Sharh Kitab Al-Tawhid, vol. 1, p. 114, 1st edition)
And Allah knows best.