The religion thing is likely always going to be one of the stickiest belief due to close link to identity and culture. I used to be quite hard line with my atheism but have mellowed with age, if someone wants to make the world a better place I'm not overly fussed what they believe happens when they die. Quite a few of my colleagues are religions and they do some of the best science out of anyone I know. I find it a little bizarre but I can attested that it doesn't get in their way. So according to pew it looks like 90% believe in a higher power but belief in a specific god has been declining (millennials are killing god!) and those that have doubts is increasing.

As for the distrust and general science knowledge I have to say I'm not sure. There is certainly a strong narrative at the moment about the whole 'my opinion beat your facts' but i'd be interested if it shows in the data, I may look into this for a post some time. As you likely know, I'm usually an optimist on issues like this but willing to accept being wrong here.