Is It Haram to Dye Your Hair Red?
Question

Is it permissible for a man to dye his hair red or yellow? What are the colours that are not allowed? With regard to young men whose hair has not turned grey, is it permissible for them to do this for the purpose of adornment only? What if a young man has the intention of following the example of the Prophet (peace and blessings of Allah be upon him) in dyeing his hair even though there is no grey hair? Will he be rewarded for that?
Praise be to Allah.Is it haram to dye your hair?
It is permissible to dye hair any colour apart from black, and there is no differentiation in this regard between old men and young men. There is nothing wrong with dyeing the hair before grey hairs appear. It says in Fatawa al-Lajnah al-Daimah (5/168): 
“Question: I saw some people using something to change the colour of their hair, making it black or red, and I saw them using something else to make curly hair straight. Is it permissible to do any of these things? Is the ruling the same for young men and old men? 
Answer: Praise be to Allah and blessings and peace be upon His Messenger and his family and Companions. There is nothing wrong with changing the hair colour to anything except black, or using something to straighten curly hair, and the ruling is the same for old men and young men, so long as harmful substances are avoided and the material used is pure and permissible. But changing the hair to pure black is not permitted, for men or for women, because the Prophet (peace and blessings of Allah be upon him) said: “Change this grey hair, but avoid black.” 
And Allah is the Source of strength. May Allah send blessings and peace upon our Prophet Muhammad and his family and Companions.” (The hadith quoted was narrated by Muslim, 2102) 
Another thing which indicates that it is not allowed to dye the hair black is the hadith narrated by Abu Dawud (4212) from Ibn 'Abbas who said: The Messenger of Allah (peace and blessings of Allah be upon him) said: “There will be people at the end of time who will dye their hair black like the crops of birds; they will never smell the fragrance of Paradise.” This hadith was classed as sahih by al-Albani in Sahih Abi Dawud. 
Is it haram to dye your hair red or yellow?
The fact that it is permissible to dye the hair red and yellow was narrated by Abu Dawud (4211) from Ibn 'Abbas who said: A man who had dyed his hair with henna passed by the Prophet (peace and blessings of Allah be upon him) and he said: “How handsome this is.” Then another who had dyed his hair with henna and katam passed by and he said, “This is more handsome.” Then another who had dyed his hair yellow passed by and he said: “This one is more handsome than all the others.” The comments in this hadith had to do with changing grey hairs to another colour, not to dyeing the hair in all cases even if it is not grey. 
Al-Albani said concerning this hadith in Mishkat al-Masabih: it is jayyid (good). 
General principle regarding adornment and beautification in Islam
We should also note the general principle with regard to matters of adornment and beautification, which is that it is not allowed to do anything that involves forbidden kinds of imitation, such as imitation of the disbelievers or of immoral people, which is haram because the Prophet (peace and blessings of Allah be upon him) said: “Whoever imitates a people is one of them.” Narrated by Abu Dawud, 4031; classed as sahih by al-Albani. 
Hence before ruling that a particular kind of dye that is asked about is permissible, we must make sure that it is not an imitation of the disbelievers or immoral people, or one of the singers or actors whom young people regard as examples to be followed.  
It is also not allowed to dye the hair in a manner that is regarded as effeminate or an imitation of women, because the Prophet (peace and blessings of Allah be upon him) forbade such imitation and cursed those who do it. (Al-Bukhari, 5435) 
Did Prophet Muhammad dye his hair?
With regard to the Prophet (peace and blessings of Allah be upon him) dyeing his hair, there is some difference of opinion as to whether he dyed his hair or not. Ibn al-Qayyim (may Allah have mercy on him) said: The Companions differed as to whether he dyed his hair.  Anas said: He did not dye his hair. Abu Hurayrah said: he did dye his hair. Hammad ibn Salamah narrated from Humayd that Anas said: I saw the hair of the Messenger of Allah (peace and blessings of Allah be upon him) dyed. Hammad said: And ‘Abd-Allah ibn Muhammad ibn ‘Aqil told me: I saw a few hairs of the Messenger of Allah (peace and blessings of Allah be upon him) in the possession of Anas ibn Malik that were dyed. 
A group (of scholars) said that the Messenger of Allah (peace and blessings of Allah be upon him) used to use a great deal of perfume, and his hair had become red from that, so people thought that he had dyed it but he had not. Abu Rithmah said: I came to the Messenger of Allah (peace and blessings of Allah be upon him) with a son of mine, and he said: “Is this your son?” I said, “Yes, I bear witness to that.” He said: “He is not responsible for your sins and you are not responsible for his sins.” He said: And I saw grey hair that had been dyed red. Al-Tirmidhi said: This is the best and clearest report that has been narrated concerning this, because the sahih reports state that the Prophet did not turn grey. Hammad ibn Salamah narrated from Sammak ibn Harb that it was said to Jabir ibn Samurah: “Was there any grey hair on the head of the Prophet?” He said: “There was no grey hair on his head except a few hairs at the parting, and when he put on perfume, its colour covered them.” (From Zad al-Ma’ad, 1/169)
Can you dye your hair when there is no grey hair? 
With regard to thinking of following the example of the Prophet (peace and blessings of Allah be upon him) in dyeing the hair when there is no grey hair , I know that there is a strong difference of opinion as to whether the Prophet (peace and blessings of Allah be upon him) did in fact dye his hair or not. 
Moreover, dyeing the hair as enjoined in the Sunnah is not something that is done for its own sake, rather it is done to change grey hair, and to be different from the Jews and Christians, because the Prophet (peace and blessings of Allah be upon him) said: “Change grey hairs and do not be like the Jews.” Narrated by al-Nasai, 4986; al-Tirmidhi, 1674. 
It was narrated by Muslim (3924) that when the Prophet (peace and blessings of Allah be upon him) saw grey hair on the head of Abu Bakr’s father, he said: “Change this with something.” According to al-Bukhari (5448) he said: “The Jews do not dye their hair, so be different from them.” 
Based on this, dyeing the hair when there is no grey hair is not Sunnah and is not regarded as following the Prophet’s (peace and blessings of Allah be upon him) example, because there is no reason to do that, and it does not serve the same shar’i interests as are achieved by dyeing grey hair. 
The most that we can say is that it is permissible so long as it does not involve imitating the kuffar or cause any harm to one's health, in which case it is haram. And Allah knows best.
And Allah knows best.