Do I use "who" or "whom" in "regardless of whom they work for"?

Substitute “he” or “him”.
They work for him.
Therefore use whom.
They don’t work for he
So don’t use who

@josie is correct, use ‘whom’.
The word you want is the object of the preposition ‘of’ and needs the objective case pronoun, in this case ‘whom’.

The above answers are correct, but the use of whom has been declining. In this case, it grates on my ears to use it. I would go with who. I doubt that anyone would call you on it.

There was a television show, Who Do You Trust?. I remember an ad for it which pointed out that it should properly be Whom Do You Trust?. The show of course retained its original name.

@LostInParadise That’s why I thought – I sort of know that it should be whom, but it feels wrong. However, as a non-native speaker, it’s hard to tell how it will come across.

@josie and @dabbler, what do you think, does it sound grating to you? In this specific case, it’s for a grant application (in the UK), so perhaps that might be extra reason to go with the “official” way?

For your grant application, as well as any other official or formal communication, it’s generally best to use the correct case.

The “whom” in the example is the object of “for”, not “of”, but otherwise the above answers are correct. Who is the subject case; whom is the object case.

I was always told it was whom in front of a vowel and who in front of a consonant…
Like my grade school and middle school english teachers told me that.

I did a google search and here is what the Oxford Dictionary people have to say about use of whom.

@SergeantQueen You were taught incorrectly. That has nothing to do with it. See the answers above.

“regardless of whom they work for” better IMHO as “regardless of for whom they work”.

I’ve pretty much dropped all uppity grammar from mos to my posts. “Whom” is one. “One” is another, as in, “One could say that the sky is blue.” I think I know when to use “whom,” but I just don’t use it. If I use it wrong I sound pretentious AND stupid.

I like talking like that to flailing, ranting conservatives though.

@zenvelo That is something up with which I will not put. ;)

@Zissou good point, thanks!

@Vincentt The incorrect usage grates on my nerves in general and I would especially expect it to be correct on any formal document like an application.
I would probably expand it to make it less awkward in that case:
...regardless of the people for whom they work…

Other possibilities:

“regardless of who employs them” says pretty much the same thing.

“regardless of their employers” is not quite the same but might work depending on the context.

Thanks for the tips everybody! I’ll go with whom then, using @dabbler‘s suggestion of expanding it to get around the stiff language.