I think somewhere in FHA guidelines there is a definition of a full bath.....which includes either a tub or shower. Look it up and refer them to that. If you wish, ask them for a modern reference for a 3/4 bath.
Banks and appraisal is how you explained it, shower or tub/shower is 1, I am from Cleveland and my dad was a Broker/appraiser, (yes in Ohio in the 1970's you could be both, on the same deal even and also the loan officer). When I started in 1978 my brain had a hard time as we called shower's 3/4 also but I finally got it. I see your in New Jersey, just explain that appraisal standard is shower is a full 1. So my question how do you guys count two .5 baths? other than explaining in the report? and when I was taught the county assessor would call a master bath with two separate toilets, his and hers with a bidet, two sinks, bath and shower a full 2 baths. Do you just call it 1 the master bath or do you call it a full "2" .
There is no such thing as a 3/4 bath. You can either take a bath in the room, or not. How about a bathroom without a commode....would it still be a toilet? And, yes I have seen several like that. The commode was in a seperate room, with a seperate door. Looked more like a closet.
A lender is not the bathroom police.