Conservatives really don't like any amendment passed the 2nd. And they absolutely hate the 13th, 14th, and 15th.
The conservatives on the supreme court have been chipping away at the 14th and 15th for the last decade, but gutting both is still one of their goals.
Coincidentally, they've functionally gutted the 4th through the Supreme Court, and are taking stabs at the 6th as well.