It's not just conflicts. Unless he divests, he will be in violation of the emoluments clause on day one. As long as he retains any sort of ownership interest in his business, and that includes continued ownership by his family which will simply be ownership by proxy, he's in the position of accepting compensation from a variety of foreign governments.
And we all know that Trump isn't going to divest. We also know that a Republican Congress isn't going to do jack about the conflicts. So what will probably happen is that Trump will be inundated by law suits on behalf of his competitors for using the unfair advantage of his office to extract concessions from foreign governments.
Eventually this is going to be such a profound distraction that something meaningful will have to be done, either divestiture or impeachment.