I don't feel threatened at the thought of transwomen in women's toilets.
However, I do not support it, because I am aware and sympathetic to the fact that many, many women do feel threatened, and that it is a slippery slope to other women-only safe spaces being compromised.
Above a certain age (the age where it is normal to go to the toilet by yourself), toilets should be used by a person with the corresponding genitals. None of the cis, "born", whatever. If you have a penis, you use the men's. If you have a vagina, you use the women's. Lots of places are introducing unisex toilets now; use them. If it's really about being validated, unisex toilets are fine as both men and women can use them. If that's not acceptable, your motives amount to little more than being able to whine about TERFs on Tumblr.
For anyone doubting the danger that TW can pose, read up on the cotton ceiling. A large proprotion of TWs believe that lesbian women should have sex with them, even though they have penises, because "we're women too". If a lesbian refuses (on the grounds that, y'know, THE TW HAS A PENIS), they're shamed for being 'transphobic'. It's an insidious, dangerous part of the transactivist agenda. I say this as someone who is LGBT, who has plenty of LGBT friends including one of my closest friends, who is trans (female to male). I say it without apology or caveat.