It's more than just about Rand. Mat thinks pretty much the same about all channellers, and it's worse with men (he will gt totally creeped out by Asha'man... he doesn't know them yet... but he might have to lead them into battle before the end...)

Mat is massively prejudiced against and frightened by channellers in general.

Jordan was slowly bringing Mat around.

Logically, Mat's prejudices should have lead him to embrace the Seanchan's vision of things, but this clashed with the rest of his values (his dislike of authority and restraints that make him see slavery as some kind of an ultimate evil; his unbringing that leads him to believe men have the duty to put themselves at risk whenever women/children are in danger etc.). More and more, he realises that they way to be "rid of Aes Sedai and the One Power" as he once wished is the Seanchan's, and that's not a solution he can morally accept. So his meeting with Tuon acted like a mirror. He saw in her what people who think channellers are dangerous and unwelcome (like he does) are really like when they make they act of their beliefs, and he didn't like it one bit.

Eventually, this should lead him to accept channellers, and deal with and overcome his fear of them. And that will leave him with the task of bringing Tuon around...

I wonder if seing a channeller pregnant and vulnerable because she's unable to channel at will, a mother like every other mother - and carrying Rand's children, might make a strong impression on Mat and make him finally see Rand and Elayne as "just humans".

I think Rand might have a harder time with Perrin than Mat. Once mat accepts Rand's channelling isn't evil or dangerous (and that saidin is clean, which Mat doesn't yet know), he doesn't have much other issues with Rand. Perrin's fears about Rand are more serious and deep than Mat's. It's Rand's "darkness" and tyranical tendencies he experienced and fears, and he fears for Faile. Contrary to appearances, I'm guessing it might be much harder to regain Perrin's friendship than Mat's (Rand, Egwene, Nynaeve, Elayne might all have a hard time accepting Mat has married a woman who enslave channellers, though. Egwene in particular might react very badly to that news, if she learns about this before Tuon comes around some).