Whether "dirt money" is attributable to an employment isn't so much a function of your personal opinions, but of the opinions of the majority of the available workforce.
A company with a truly appalling reputation may have to pay over the odds to get work done, but if many others don't see it that way then the wage may simply be the ordinary market rate.
When you say "if the company is oppressive enough ideologically, I might end up resigning before securing a new position", I'd be wondering what sort of "ideological oppression" you'd be expecting, if not merely the standard kinds such as ideologies of economic exploitation and hostility to collective bargaining (e.g. what one finds with Amazon or Uber).
And look at this from the company's point of view. Your objections and flightiness don't make you a more valuable worker, but if anything a less valuable one (than an employee with full confidence in them). If you were perfectly honest with your rationale and perceptions of them, in order to justify your pay demands, they'd probably want to cut your pay rather than increase it. In fact, they'd probably ask, why did you even apply for such a job?
The possibility of higher pay does not clearly explain your application, because you rationalise it merely as insurance for the risks you are running, so you could just as easily accept lower pay elsewhere and run no such risks, and keep a clean conscience.
There is also a contradiction between the strong ideological objections you claim to have, and the fact that you're perfectly willing to risk being caught working for a firm who turn out to be ideological undesirables, so long as they compensate you ahead of time for the public soiling of your own reputation that will result.
The hallmark of strong ideology is that it is inconvertible with personal advantage, and that a cash payment from the devil doesn't make up for being ideologically embarrassed. And if the pay premium you seek is seen less as a personal advantage and more as a penalty to an employer with an as-yet unclear nature, then that is a market for lemons, since the angel will be penalised unfairly by your lack of confidence, and the devil insufficiently penalised by your giving the benefit of the doubt!
If you really want to be a mercenary getting paid for dirty work, then be honest at the interview that you have principles available for sale, that it is other people's opinions that you want compensation for, and you've come to discuss the terms the devil may be offering for a deal. And if it emerges publicly that they are the devil, then you won't be walking out due to your own principles, you'll be walking out because at that point they still aren't paying you enough to deal with the opprobrium you sustain from others.
They may insist they are not the devil, and refuse a deal on any terms which suggest that they are, but then you've found out what you wanted to know.