How simplistic.
Where I grew up, political and religious views were totally polarised, to the point of violence.
I've never been all that interested in either set of views. I have never seen it as a barrier to friendships. So long as you have an understanding that these subjects are 'no trespass' zones, you can actually get on pretty well with someone whose views on these subjects are diametrically opposed to yours!
I'm not a fan of cossetting your little darlings to only hear only your views, and that they should only mix with your clones. Teach them well at home and they will soon shut down anything they see as racism, same as mine learned about making friends across a huge chasm in terms of religion and politics.
Happily, none of my three give either a second thought. It's just not on their radar. Discrimination, racism, transgenderism - those are issues that exercise their minds.
This woman is most likely the product of her upbringing too. Maybe you could be a good influence on her, challenge her thinking, if you wanted to?
However, in this situation, I would take a step back. You don't have to be bezzies with your children's parents and it's probably best in many ways if you're not. I would not be socialising with her other than maybe a coffee when either of you drop off at the other's house, and I would not go on any sort of holiday with them. That has disaster written all over it, and could wreck your children's friendship. Maybe this friend will be a 'forever' friend (my 25 yr old has been besties with her friend since they were 3) but most likely they will move on and make other friends. It's not sensible to get this invested.