While the language is a bit strong, and a few statements questionable, the basis of the article is correct, in my view.
Like Mr. Scalise, I am from Louisiana. There is no way, absolutely no way, he didn't know that group he gave a speech to was a white supremacist group. Affiliated with the group, David Duke, mentioned in the article as a prior rep. of Louisiana, is famous in Louisiana. He ran unsuccessfuly, as a Republican, for governor. He had been a Grand Wizard in the Ku Klux Klan. Scalise would have been well acquainted with Duke, and in fact, information has turned up that he knew Duke personally.
The Republican Party, especially after the way many of its members acted during Obama's Presidency, has this particular problem. It's true. Much damage has been done to their reputation. But to put it in perspective, they don't care. As long as they win elections (whatever the means), that's what matters.
Look at the posts in response to your OP. The article is about the "problem" of the Republican Party. A problem of appearance, perception, possibly even proof. But the posters don't even mention that. Not one "I don't think there is that perception" or "If that's the perception, how can we fix that?" THEY cannot say the problem doesn't exist. It can only be stated by someone who is not of that party, who can say whether or not s/he perceives the Republican Party that way.
By everything we see and read and hear and experience, the Republicans are perceived this way, and do have that problem the article discusses. To fix that, they would have to start with, say, not naming as one of their leaders in Congress a white male who gives speeches to white supremacist groups. That would be a start.