I don't believe that anyone is literally 'born in the wrong body' - I am not religious and I don't believe in gendered souls.
How literal minded is this?
"Born in the wrong body" is just a euphemism to describe the feeling of gender dysphoria.
TRAs want to remove sex segregated spaces, many of which are there for the protection of women and girls. This sounds like men's rights to me.
I've never heard a MRA campaign for the removal of sex-segregated spaces. Virtually all MRAs I've ever seen have rolled their eyes at these new "gender neutral toilets" we've all seen.
I actually arrived here after being signposted to the 'hardcore feminists on mumsnet' by someone on another forum which had gone from general discussion to being quite a woman-hating place.
What board is this?
I imagine a MRA message board to be like that, or maybe an even more extreme version, so I wouldn't seek one out. It was pretty unpleasant. I'm much more at home here.
Have you BEEN to one?
To me, it seems you are just imaging MRAs to be what you want them to be (ie. people you hate who believe the polar opposite of what you believe). You should actually browse their boards to see how they think. I could name a few, but I'm not sure if the website's rules allow me to do so.
From what I've seen, MRAs typically have very traditional, conservative values. They lament the existence of women who don't want marriage, families, and children, and clap their hands with glee whenever this lifestyle backfires. For example, they love digging up articles about career women who can't have children because their frozen eggs didn't survive the thawing process, and say she wouldn't have had that problem if she had settled down and married sooner. Given their conservative, traditional values, they despise gay people, are usually anti-abortion... and have a strong dislike of transgender people.