So I don't consider myself rightwing - but I certainly read & watch a lot of content by those who oppose the extremes of modern progressive politics. There is a argument with which we console ourselves, and I'm not sure it holds water.
The argument takes this form: feminists complaining about mansplaining weaken feminism because they imply that women are so weak that they need to be protected from male arguments. A similar assertion is that positive discrimination and "offence politics" are themselves racist because they imply that ethnic minorities are too stupid to get jobs for themselves and, again, need protection from offence (by authoritarian, anti-free-speech laws)
The appalling logic of progressives might weaken the logical framework they are putting forward - but political power, as we know, is not won by presenting the most logical argument, but by either persuading people with arguments (however specious) and traducing or threatening anyone who disagrees. In this, feminists and the "everything is racist" mob are preeminent: their approach to politics is entirely based on accusations of hatred and arguments that are just plausible enough that the more articulate people* in their camp can persuade themselves that they are right.
In my first example above, the more bonkers feminists may continue to argue that women need to be protected from interruptions, that men aren't allowed to express a view on the abortion issue, and that womens' prisons should be closed, and at the same time they will claim that they "only want equality". Some of us will laugh at what nonsense this is, and then we will watch and wonder why those who rule us do exactly what the activists want
So the progressive cult may still be successful politically as what they say gets less and less internally consistent. It may take a long time - and a lot of work for the rest of us - for their intellectual dishonesty to be widely recognised. As much as anything else, it's a matter of removing a self-selecting group from power, and seeing as they are very rich, this could be difficult
* note that I did not say "the more intelligent people in their camp"