no, it's the other way around. anime is popular in a geeky/nerdy subculture, these subcultures attract a lot of people including transgender people because anime is escapism and no matter what problems you have in life, anime can take them away for a little. anime fans have a sense of community around the shows that they like, and that's appealing for anyone who feels like they don't fit in in the real world.
there are also many characters in anime who are transgender such as grell from black butler, or who don't conform to gender norms such as felix from re:zero who is a boy but dresses like a girl because he wants to. it's nice for them to have characters like that without their whole character being about how much of a minority they are which is more common in western media.
so tldr, no nothing is turning anyone transgender. trans people have a mental illness called gender dysphoria that is helped by transitioning. trans people just happen to like anime for many of the same reasons nerds like it and for characters who are regular people that also happen to be trans.