Answering as a non-religious gay person - No.
Whilst I am aware of the apparent dislike of homosexuality in the Bible, Koran, Torah etc - I am also aware of the context that the verses used to condemn are presented within - that is, very little context if any, as they are usually cherry picked to suit one's argument.
That being said - people find faith wherever they find it - so, if that means that they have found Christianity, Islam, or Judaism, is the religion that resonates with them, that makes the world make sense to them - then to change this merely because one's faith MAY disagree with a significant part of one's self is likely to be damaging.
Merely because some people's interpretations of a Holy text may insinuate that one's innate (meaning - not chosen) sexuality or gender orientation is less than desirable for which ever version of God they believe in, does not mean that their God does not love them as they are - we are all, of course, made in His image, are we not? Are we to say that He has made mistakes?
What I would suggest these people do is find a Church, Mosque or Synagogue that is open to LGBT people, a denomination that has these open places of worship - and attend there. There are many Christian denominations that accept LGBT into their 'flock'. Why? Because, again, it is ONE person (pastor, Imam, Rabbi) interpretation - you should not base your life's worth on the interpretation of one person who is NOT yr God - your relationship with your God/s is personal, and no one can tell you its wrong (those who do...who are they really serving?)
One is not only one's sexual orientation or gender identity. One is also not only one's faith. One can, and should, find a way for the two to co-exist within one's self.
I am not religious, because I have not found a faith that resonates with me. Not because I am gay, because there are plenty of faiths that would accept my homosexuality with open arms, but because there are none who speak to my core - I am more than my sexuality, and more than my faith (or...in my case, lack thereof).
Sure, Buddhism is accepting, so are many Pagan faiths, so are some Christian branches. So, if they are something that resonates with you - by all means go ahead, but if they don't - there is no reason to change
(However, if your faith is striving to make you feel worthless, unworthy of love, for something you cannot change (sexual orientation etc). then are they really the loving religion claimed?)