Honestly, I think this is being a bit generous to the right. Maybe the right thirty years ago was as you describe, but not anymore. Major right-wing institutions have done little to nothing to push back these people supposedly "adopting a right-wing persona", because they realized these people are an amazing way to push the social narrative to the right and amass more power.

I think respectable right-wing politics are dead (or at the very least, on life-support) in a post-Trump era. The Republican Party was initially pretty hostile to Trump and his style of politics, until they realized they could exploit it to garner more power.

I highly recommend watching Innuendo Studio's video on YouTube, The Alt-Right Playbook: You Go High, We Go Low. The whole series is worth a watch, but this video in particular shows how good faith attempts to reach across the political spectrum are easily exploited by fascists.