You may be correct - it will ultimately be decided by the courts. Unfortunately, if you run a business you are not allowed to ignore the EEOC just because OSHA puts out a rule. I don't have a strong personal opinion about this issue either way, but I do have to evaluate my risk of getting sued from all angles. Maybe the EEOC will modify their rules to match OSHA.
The EEOC rules, which are already on the books, are here under section "K":
EEOC
I don't like being used as Biden's enforcer just because I run a company, but such is life.