What's more important...

Depending on which media people consume, both sides can think they have the truth. Some people think it’s true that vaccines are dodgy, others think it’s true that vaccines are lifesavers. It’s extremely difficult to have any fixed position at the moment about anything as information is often scarce and incomplete. So to the question, I never let media generated information create divisions among me and my friends.

I've made many friends and met women from all over the country fighting this war on women. The truth will out!

Do you think they are having similar internal battles? I suspect not, if they're shunning you based on rumour. If not, they mean more to you than you do to them.
Put another way, their loyalty to an idea is greater than their loyalty to you.
Doesn't sound like a friendship it's worth abandoning your principles for!

I think truth is important. Its who you are essentially but you don't always have to say it. Some deeply held 'truths' are opinions.
With my family and closest friends I can be totally up front and honest about myself, we may disagree about some things but are able to talk about them honesty.
With other friends not so much. Subjects might come up where we disagree but I might be non-committal or change the subject to keep the peace. If directly asked, I won't lie though.

So difficult. Friends - and family in my case too - are obviously important. But so is personal integrity and not colluding. And not giving in to what feels like mass gaslighting.
I've taken both stances, arguing and shutting up. There's no comfortable place, it's an ongoing dynamic. I try to take a long view - I'll avoid the subject but hope that as opinions shift we can again open up about it.
Meanwhile there's a certain emotional distance but not total estrangement.
Sorry @wrongthinker don't know if that's any help.

I do have lots of friends, I suspect many are the same truth seeking flavour of autism.

I'm autistic, the truth is very important to me.