My guess is that the issue is more about the reverence for both the named bible (Trump bible) and the signature. There are those who might equate that level of reverence with graven images.
If someone worships that book BECAUSE it has Trump's name on it, that sin of idolatry is on that foolish person. No doubt.
What Trump did is tacky. I wouldn't do it. Nothing sinful about it. We don't have to look far to see Trump sin. This isn't it.