I looked and the common pattern I see is that conservative parties are actually several smaller parties stacked in a trenchcoat, pretending to have a common direction, but too scared of adressing inner conflict. They still hope they can continue to uphold a facade of unity by pandering to the rightwingers.
It’s not very effective. But I see that as a result of group-psychology and basic human incompetence, not as explicitly agreeing with fascist values.
Everyone should be aware that the final say is provided by Putin. And is a foregone conclusion - for purely tactical and propaganda reasons, the official version will be that Prigozhin is dead. And nobody will contest that - least of all Prigozhin himself.