It’s not just that. What you mentioned is a real phenomenon, but not always the case.

One other reason is when right-wing parties don’t realize that their policies are contradictory in practice. This is common in syncretic politics, like Classical Fascism, which has strong roots in both Syndicalism and Nationalism. Mussolini’s class collaborative corporatism [as in corpus, ‘body’] is a policy which sounded progressive on paper but in reality did not prevent the worker exploitation it aimed to lessen.

Another is that even reactionaries can recognize some good ideas, as long as it doesn’t contradict their personal values. I personally know conservatives with pro-environmental policies, because they appreciate and care about the ecosystem and our food supply chain. I know another strong conservative who is anti-privatization but consistently votes for a pro-privatization party! Politics is complex, not a team sport where every voter toes a line.