Should not be a problem if they keep meat and dairy apart and prepare them in different work spaces. Their sandwiches are not all that great, anyway, but are inexpensive and filling.
I think they just forego the cheese entirely because (a) it would be quite a hassle keeping two separate kitchens/workspaces in a place like a Subway, and (b) with the exception of a couple of vegetarian sandwiches, most of the time that cheese is used in a Subway sandwich, it is in a meat + cheese combination. So, no reason to bother even keeping cheese around. (For the same reason, there are a bunch of Kosher Dunkin’ Donuts around me, none of which serve meat)