I don't see any parallels between homosexuality and transgenderism. Homosexuality occurs widely in nature. It's innate. You get gay animals, even gay birds. However being transgender is entirely confined to human beings, because gender is a social construct.
Another difference is that gender is oppressive whereas being gay is not. Gay people don't demand anything of anyone, just to be allowed to get on with their lives. In comparison, male trans activists want to infringe on women's rights and demand that we validate their identities however bizarre these might be. Stefonknee anyone?
There's currently an explosion in the number of both teenage and adult transitioners. Trans is very, very fashionable and part of the reason for the steep rise in numbers is that the trans umbrella now includes fetishistic cross dressers as well as what used to be called transsexuals. Its rise also seems to stem from medical advances, an antifeminist backlash that means gender is being enforced with a heavy hand, and a horrifying increase in the amount of porn consumed, specifically lesbian and shemale/sissyfication porn. People say young women transition out of self-hatred, whereas a lot of adult men transition because of porn.
Although there are some societies which recognize a third gender, there is no history of transgender identity being a natural feature in all societies, whereas homosexuality occurs in all times and places. Many people speculate that in a gender-free society no one would be trans.
I first marched for gay rights when I was 14. Like millions of other people I felt passionately that people should be free to be true to themselves. That doesn't appear to be what's happening in a lot of cases where people transition. People like Miranda Yardley know they're male. Others try to insist they have a female penis. This group is characterized by self-delusion, denial and, when crossed, astonishing levels of narcissistic rage.