Ok Here it goes, please be aware, I am probably going to say something that isn't going to agree with your person. But try to hear me out.
Alright, here we go.
I grew up in a self-isolating Christian group and I've had a falling-out with it. There are many people in the group that I care strongly about and there are some beliefs that have stayed with me, but there's just something about insisting that evolution is fake that doesn't sit well with a biology student... And something about saying transgender people are delusional that doesn't sit well with a trans man. So here I am, with a spirituality-shaped hole in my heart.
Evolution is quite well documented, while the extent that some people take it, seems a little far fetched without some kind of intervention or direction, it is clearly a well established theory with enough evidence to believe. I would say there are many Jews and Christians that have no problem with the idea. Most Muslims would say Science has shown great likelihood, therefore most of us accept it as a probable.
So here goes the part that starts off with the bad, In Islam, much as it is in Christianity and Judaism, Homosexuality is a sin in its action. One could argue the idea that had the seed of the feeling behind it is stemmed from a crossing of the straight path onto the wrong path, but that would be something of an issue with past. This same issue is true of the Transgender idea. I'm sure as a biology student you are aware of what organs and chromosomes separate the sexes. The hormones can be synthesized (although I'm not sure how healthy that really is), the genitalia can be removed/changed cosmetically, and of course clothing is purely optional as to what one would wear, but none of this changes the Chromosomal makeup of you. There has also (to my knowledge) never been a true gender swap where a person changes their original makeup into the other with functional reproductive organs. So that leads to the debate, is it a choice or are you born with it, or is it a product of environmental inputs in your life. I'm in the 3rd boat honestly. I think those feelings are input through some trigger in your life, and whether you wanted it or not, you were drawn to the idea. Much like racists, bigots, etc are usually stimulated by parents or some act that solidifies their idea. IMO this is the common thread among all the LGBT community. Somewhere a trigger was pulled and the idea that this could be ok or right to that person was pulled by an event in their life.
Now what does the scriptural Jews (unlike the reformed Jews who are pretty open to anything) and Christians say about the LGB idea, it is a sin, The bible is very clear that the action is disgusting to God. And if read literally commands to kill the perpetrators can be found. The Quran offers a slightly different approach. You see for Human actions, one must produce witnesses if you make an accusation. Sodomy, much like most "crimes" requires 2 witnesses. Unless one is displaying their actions in public, how would anyone know? In Islam public displays of affection are generally frowned upon and most Shariah scholars will say it is Haram (forbidden) (this includes public sexual actions, kissing, caressing, etc. with Holding hands with ones wife being debatable). Also seeking to see someone else in these acts are Haram. So if you keep it in your bedroom, hidden from view, it is impossible to prove, and therefore anyone who accuses the actions would be committing a great sin (bearing false witness). This would also mitigate the likelihood that one would ever see people acting like this and likely decrease the ideas from making it widespread. Children wouldn't even be exposed to sexual actions until they are married, to which they would never have seen anything to think this might not be right.
The Trans issue is slightly different. Given the Social structures of Islam, and the belief that Marriage is an important thing, a man who acts as a woman, offers nothing legal to a man. A woman dressed as a man (please stick to biologic descriptions, the swapped genders thing makes it tough to follow) would have nothing to bring to a marriage as she would not be able to impregnate her wife. These of course assume the trans person is marrying a non-trans. It also plays issues with Hijab usage, and social roles, and social interactions with others. From a strictly Shariah standpoint the trans person would not be able to legally function in society other than as a loner.
I have heard of a Hadith (and please if anyone knows the Hadith and it's location please feel free to post it) Where upon Mouhammed's (PBUH) acquiring of influence over a town a group of Eunuchs came to him to accept Islam (body mutilation is forbidden outside of circumcision where males is required and women is very slightly allowed under heavy regulation). His response was that they were free to accept Islam, but they would dwell separated from the rest of the Muslims (although it talks of their living away, it never seems to forbid them from enterring the city for work or trade).
That's all the time I got atm. I hope it is helpful in enlightening you, and whether you like or dislike this view, it is our view.