Is a non - military ID holding person allowed to go into the px with a military ID holding person? Or are they not allowed in at all?

Yes they can't make a purchase

Anyone can go in. At random times in the year they check all IDs upon entry, and I believe non military people have to be accompanied by a military ID holder. They require the military ID to match the name on the credit/debit card as well, as a side note. Only the military ID holder can make a purchase.