Surely the same should be the case for Marxists? Uncle Karl discusses "the ruthless criticism of all that exists", after all. The whole basis of the Marxist method is the material positionality of all the makers of theory. There is no "God's eye view" or Platonic realm of ideal forms. All ideas come from the material position of those who have the ideas, who discuss them and who propagate them. So a Marxist scholar-activist should be reflexive in practice as a matter of course. And a Marxist organisation, in turn, should encourage different points of view within itself, to welcome debate on its very existence and ways of organising.
... but they don't, do they? Because questioning organisational routines is the first step towards dissolving the organisation. Because habitual adherence to authority and routine is an "opiate" or "painkiller", which provides a feeling of security, which holds back the unpleasant feeling of actually having to deal with the howling menace of neoliberal globalised capitalist commodity culture and the total failure of the actually existing far left to do anything about it. Some organisations actually forbid self-reflexive discussion of the organisation - either because it's "navel gazing" irrelevant to "the workers", or out of honestly admitting that if we stopped to think about what we were doing, we wouldn't be doing anything. Which should make anyone who was honest think: then is it worth doing at all? Is mindless activity better than honest befuddlement?
Incidentally, check out the rhetorical move about "the workers" above. The sheer fact of the matter is that the actually existing Anglophone far left tends to be composed of white people with high levels of formal education and thus often a mildly privileged class position. But the essential dishonesty lies in refusing the very basic form of reflexivity involved in accepting this, and instead either claiming to speak for an imaginary "Worker-with-a-capital-W" subject who is in manual labour and has a very low level of cultural capital, or indulging in a guilt trip of not being a Worker-with-a-capital-W, or attempting to somehow become one by adopting a fetishised version of the culture of that layer of the class. This kind of "cultural guilt" is just as cringeworthy and destructive of a real politics of solidarity as "white guilt".
An honest position for cultural-capital-heavy Marxists would be based on being in solidarity with other sections of the working class while not denying one's own positionality. The romantic fiction indulged in by some groups that they are "declassed intellectuals" is precisely a refusal of the self-awareness of their real class position which would be step 1 of a real Marxist praxis.
Incidentally, when seen properly, the insistence on spiritual traditions of having a "master" or "guru" is an expression of reflexivity, in the sense that when you're just starting out, you have NO WAY to actually "look at yourself". Eventually, you can find the "master inside yourself", but only after internalising that very external viewpoint on which you have originally required. You can call it God, if you like.