A woman asking about the religious commitment of one who comes to propose marriage to her is not making things difficult
Question

                I am a religiously-committed young woman, praise be to Allaah. I am 25 years old. The problem is that every time someone comes to propose marriage to me, I ask my mother to ask his family some questions, like Does he pray? Does he smoke? Is he one of those who are interested in music and TV? Because those who come to propose to me are not religiously-committed. My mother says to me, “You are making it difficult.” She is afraid that I will miss out on marriage because of my stipulating conditions.
 Am I wrong? What do you advise me to do? I am afraid that I am dreaming of a righteous man when there are no such men. And Allaah knows best.
Praise be to Allah.You are not wrong and you are not making things difficult, rather you are doing well to ask about the religious commitment and character of these suitors. This is what your family should in fact be doing; it is not permissible for them to object to your doing that, rather they should support you in it. 
Islam enjoined making a good choice of husband and wife. The common factor in choosing is good character and religious commitment. A woman is too weak to be steadfast in her religious commitment if she marries someone who is lacking in character and religious commitment 
Hence our advice to your family is to support you in this matter. Seek the help of Allaah with patience, prayer and du’aa’, and we ask Allaah to bless you with a righteous husband. 
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allaah have mercy on him) was asked about the most important qualities for which a girl should choose her husband. 
He replied: 
The most important qualities for which a woman should choose a man who proposes marriage are a good character and religious commitment. As for wealth and lineage, these are secondary matters. The most important thing is that the suitor should be religiously-committed and of good character, because the woman will not lose out with one who is religiously-committed and of good character: if he keeps her, he will keep her in a good and proper manner and if he lets her go, he will let her go with kindness. Moreover, a man who is religiously-committed and of good character will be a blessing to her and her children; she will learn morals and religious knowledge from him. But if he is other than that, then she must keep away from him, especially those who take the matter of praying lightly, or who are known to drink alcohol – Allaah forbid. As for those who do not pray at all, they are kaafirs and it is not permissible for them to marry believing women. The point is that the woman should focus on character and religious commitment. As for good lineage, this is preferable, because the Messenger (peace and blessings of Allaah be upon him) said: “If there comes to you one with whose character and religious commitment you are pleased, then give (your daughter or female relative under your care) to him in marriage…” But if there is social compatibility too, that is preferable. 
Fataawa al-Mar’ah al-Muslimah, 2/702 
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allaah have mercy on him) was also asked about a man who proposed marriage to another man’s daughter. When he asked about him, he found out that he did not pray, and the one who was asked about responded by saying: “Allaah may guide him.” Should they go ahead with this marriage? 
He replied: 
If the one who is proposing marriage does not pray in congregation, then he is an evildoer who is disobeying Allaah and His Messenger, and going against the Muslim consensus, which is that offering prayer in congregation is one of the best of acts of worship. Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said in Majmoo’ al-Fataawa (23/222): The scholars are agreed that it – i.e., praying in congregation – is one of the most important and best of acts of worship, and one of the greatest symbols of Islam. End quote. 
But this evildoing does not put him beyond the pale of Islam, so it is permissible for him to marry a Muslim woman, but someone else who adheres to Islam and is of an upright character would be better than him, even if he is less wealthy and of a lesser lineage, as it says in the hadeeth: “If there comes to you one with whose character and religious commitment you are pleased, then give (your daughter or female relative under your care) to him in marriage.” They said: “O Messenger of Allaah, even if he falls short with regard to wealth and compatibility.” He said: “If there comes to you one with whose character and religious commitment you are pleased, then give (your daughter or female relative under your care) to him in marriage” three times. Narrated by al-Tirmidhi. And it is proven in al-Saheehayn and elsewhere from the hadeeth of Abu Hurayrah that the Prophet (peace and blessings of Allaah be upon him) said: “Women may be married for four things: their wealth, their lineage, their beauty and their religious commitment. Choose the one who is religiously-committed, may your hands be rubbed with dust (i.e., may your prosper).” 
These two ahaadeeth indicate that the best things to pay attention to are religious commitment and good character in both the man and the woman. The guardian who fears Allaah and understands his responsibility is to pay attention to the advice of the Prophet (peace and blessings of Allaah be upon him, because he will be asked about that on the Day of Resurrection. Allaah says (interpretation of the meaning): 
“And (remember) the Day (Allaah) will call to them, and say: ‘What answer gave you to the Messengers?’”
[al-Qasas 28:65] 
“Then surely, We shall question those (people) to whom it (the Book) was sent and verily, We shall question the Messengers”
[al-A’raaf 7:6]
But if the one who is proposing marriage does not pray at all, neither in congregation nor on his own, then he is a kaafir who is beyond the pale of Islam. He should be asked to repent, and if he repents and starts to pray, Allaah will accept his repentance if his repentance is sincere and truly for the sake of Allaah. Otherwise he should be executed as a kaafir and apostate, and he should not be buried in the Muslim graveyard, and he should not be washed or shrouded, or the funeral prayer offered for him. The evidence that he is a kaafir is to be found in the Book of Allaah, may He be exalted, and in the Sunnah of the Messenger of Allaah (peace and blessings of Allaah be upon him) – and he quoted the evidence concerning one who does not pray, then he said: 
As it is clear from the texts of the Qur’aan and Sunnah that the one who not pray is a kaafir whose kufr puts him beyond the pale of Islam, then it is not permissible for him to marry a Muslim woman, based on the texts and on scholarly consensus. Allaah says (interpretation of the meaning): 
“And do not marry Al-Mushrikaat (idolatresses) till they believe (worship Allaah Alone). And indeed a slave woman who believes is better than a (free) Mushrikah (idolatress), even though she pleases you”
[al-Baqarah 2:221]
And Allaah said concerning the women who migrated for the sake of Allaah (al-muhajiraat) (interpretation of the meaning): 
“O you who believe! When believing women come to you as emigrants, examine them; Allaah knows best as to their Faith, then if you ascertain that they are true believers send them not back to the disbelievers. They are not lawful (wives) for the disbelievers nor are the disbelievers lawful (husbands) for them”
[al-Mumtahanah 60:10]
The Muslims are unanimously agreed on what is indicated by these two texts, namely that it is haraam for a Muslim woman to marry a kaafir. Based on this, if a man gives his daughter or other female relative who is under his care in marriage to a man who does not pray, that marriage is not valid, and the woman does not become permissible to the man by means of that contract, because it is a contract which is not in accordance with the command of Allaah, may He be exalted, and His Messenger. It is proven from the hadeeth of ‘Aa’ishah (may Allaah be pleased with her) that the Prophet (peace and blessings of Allaah be upon him) said: “Whoever does an action that is not in accordance with this matter of ours will have it rejected.” 
So the marriage is to be annulled if the husband does not pray, unless he repents and comes back to Islam by starting to pray.  
To sum up: With regard to this suitor who does not pray, if he does not pray in congregation then he is an evildoer who does not become a kaafir thereby, so it is permissible to marry him in this case, but one who is religiously committed and of good character is better than him. If he does not pray at all, neither with the congregation nor on his own, then he is a kaafir and apostate who is beyond the pale of Islam; it is not permissible for him to marry a Muslim woman under any circumstances, unless he repents sincerely and prays and adheres to Islam. 
With regard to what is mentioned in the question about the woman’s father asking about him and the one who was asked about saying, “Allaah may guide him,” the future is known to Allaah and control of it is in His hand. We are responsible for what we know in the present, and what we know about the suitor right now is that he is a kaafir and it is not permissible for him to marry a Muslim woman. But we hope that Allaah will guide him and bring him back to Islam, so that he will be able to marry Muslim women; and that is not difficult for Allaah. 
Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen, 12/question no. 31 
Conclusion: You have to be patient until Allaah blesses you with a righteous husband. What you are doing by asking and finding out about the character and religious commitment of suitors is something that is prescribed in Islam, in fact it is obligatory for you and your guardians. If the suitor does not pray, then any marriage contract is not valid, because not praying is kufr that puts one beyond the pale of Islam. Smoking, shaving the beard and listening to music are all haraam actions and they are legitimate reasons for refusing a suitor if he does those things. 
We ask Allaah to guide you and make you steadfast in obedience to Him, and to bless you with a righteous husband and good children. 
And Allaah knows best.