You're missing that the hyperpartisan tribalism, which has been the default and dominant Republican party strategy since Gingrich in the mid-90s, seeks to attack and exploit every possible angle and every possible weakness of the "enemy", fair or unfair, whether it helps or hurts the country, whether it's divisive or unifying, whether it's true or false. If you can use it for advantage, you use it.

Trump plays that song better than most, whatever else his failings are, and Birtherism fits the bill.

Undoing Obama policies doesn't seem to have had nearly as much to do with Obama being black (how many times did they fail with "Obamacare" due to its popularity?) as being able to look busy, undo "socialism", and benefit special interests.

This isn't to say that there was no impact at all. But compared to the natural evolution of hyperpartisanship, I don't think it explains very much.