The headline is wrong. It's not "Trump's Republican Party". It is the voters Republican Party, as it should be. Sanford's loss wasn't due to Trump not liking being criticized. It was due to the voters, ordinary South Carolignians, not liking that criticism.
I don't think anyone is expecting/demanding that GOP politicians all take the affirmative step of praising Trump. Even most of his supporters occasionally cringe at the things he says. But there is a big difference between not praising everything he says (and just remaining silent), and choosing to publicly criticize it. The latter is perceived as aiding Democrats who have been trying to kneecap his Presidency since day one. And since a lot of those GOP voters don't like the idea of Democrats trying to cripple the Administration, they don't take very kindly to elected Republicans who go out of their way to criticize him.