You know this already, but all of this is because the Republican primary is the real election. Primary voters are going to pick the most conservative candidate, full stop. Ken Paxton coming out and saying someone isn't sufficiently conservative is a devastating attack in the context of a Republican primary.
But then so what in the general election? Of course the Democrat will point out that the Republican candidate is an unhinged reactionary, but your average Republican voter will just chalk that up to partisan mudslinging. In reality, Karen from the Woodlands and Billy Bob from Odessa know fuckall about the candidates for Court of Criminal Appeals (to be fair, I barely do either). They see an (R) and a (D) on the ballot, know that they're Republican voters, and mark the person with an (R).
The question is how far can the state Republican party go before people start to notice, care, and vote accordingly? I'm a pessimist at heart, so I tend to believe the line is pretty fucking far. My guess is that to the extent that people even pay attention, there's a lot of the same rationalization we saw with Trump - "listen, I don't necessarily agree with everything Ken Paxton does, but I could never vote for a Democrat that wants to flood our country with transgender illegal immigrants and allow abortion on demand at 39 weeks".