There is no impact simply because governors have no say in the impeachment or removal of presidents.
I expect most of them to stay silent on the issue.
They'll probably try to stay silent on the issue, but will the media and their opponents let them? All politics is national these days. I expect all the GOP candidates to hammer this home until the very end. I'd certainly consider it a huge gift if I was one of them. Bevin was running as a pro-Trump one trick pony even before this, so I imagine that strategy will be taken into overdrive now.
It could also have the unintended consequence of both firing up the GOP base, making them more likely to vote AND less likely to cross over and vote for a Democrat. Same for the Democratic base, but that's going to be far more useful in Virginia than a place like Kentucky, lol.
Of cause they can stay silent on the issue.
eg.
"I am running for governor of [state name]. It is not my job to determine what the president did or did not do. What I am concerned with are [some local matters in the states]."
Headline: [Candidate] Refuses To Condemn Impeachment
