I'm not sure the Christians in my church who dislike President Trump are intentionally claiming the moral high ground. But I think they're stuck in the old paradigm that a Republican who promises to pursue Christian-friendly policies must be virtuous and a Christian himself. Of note to me is that the people I heard grumbling about him are senior citizens.
I'm actually of the opinion that he's likely not saved, yet, but seems to be changing more and more every day. I think God is drawing him. I hope so.
That said, It's irrelevant to me if a government official is a Christian or not. Some Christians make terrible governing authorities, and some unbelievers actually follow God's plan for governments better than many believers. I'll never vote in accordance with identity. It's all about what they do.