I imagine that if we were to impeach the president — any president — it would shake up the markets briefly since most things do. Then when they see that the sky isn’t falling, it’s business as usual.
As to whether Cheeto-head has had any direct influence, though, nah. My brother, who is a CFO for a major company (and incidentally a Republican but not a Trump supporter), has always said that there’s a four-year lag — so our current bull market is due once again to Obama. I do suppose that loosening regulations would have a somewhat more immediate effect, albeit to the detriment of employees. Overall, though, I actually fear the orange dude’s eventual influence on the market, for all the reasons you mention.