Remjet from experience doesn't ruin chemistry. You just need to filter your chemistry, which if you're running replenished you need to do anyway.
If the film was so easily damaged from remjet particles floating in solution, a wet remjet bath the film passed through wouldn't work. Please see the Kodak document on motion picture processing, which shows processor design.
If you agitate the hell out of the remjet softening bath with the film, and rinse/wash, you shouldn't have much remjet come off in other solutions during regular agitation anyway.