I am pretty sure that "мне по хрену" is a parody on "мне по плечу" (literally "fits my shoulder" but means "doable to me / within my powers"). Russian people coin new expressions with such witticisms all the time.
So, reproducing the same parody in English, one could say "fits my wiener". Horseradish here being an obscenity-avoiding euphemism for c*ck (like English "wiener"), not the plant (just like all the sausages and cucumbers in the other languages).
As I native, I would assume that "мне по хрену"/"мне похрен" is an euphemism of the more rough variant "мне похуй" (it is up to my dick, same height as my dick).
It's also definitely a ‘minced oath’ for ‘похуй’—which involves the dick and a prefix/preposition that is basically random, as usual for abstract idiomatic expressions in various languages.
For general absence of fucks, there's also the suitable ‘it doesn't fuck me’.
Yes, the horseradish here is a word that sounds similar to dick, and yet is inoffensive enough not to be tabooed. A similar kind of substitution in English would be heck instead of hell, or shoot instead of shit.
Well, that's a one way to say it for sure, but that's almost the most delicate way, lol.