I think the fact that they don't use modern technology would suggest that they probably don't know what's going on as far as BLM is concerned. Let's be real here; limited exposure to the media probably means all they see is stories praising the concept of Black lives matter, as opposed to what the organization itself stands for, which is Marxism, which I imagine the Amish are against.
As for them supporting Trump, they probably don't know too much more about him and national politics than they do BLM, other than the negative impact Democrats and their policies have directly had on them. I can't imagine a group that would be more concerned about govt over-reach, and prohibiting worship (i.e. limiting religious freedom) than a group like the Amish, or even the Quakers.