As long as they are competent and safe divers, who cares if they're DIR or not. If you're doing dives in areas that are challenging, care and familiarity of/with the buddy and his abilities is probably more essential... but than again, I always dive with the same DIR buddy.....
I would disagree for cave/technical dives. For these cases, I am 99% going to dive with someone that has had GUE (or equivalent) training.
I do not want to to a tech dive with someone that has their eye glued to their computer, who has a different idea of deco than me, different gas selection, or that has a different opinion on what "team diving" means etc. etc. etc.
For recreational dives, it also depends. I can, will and have dived with non-DIR/GUE divers on recreational dives, but I generally need to get a sense they will stay close, and follow the same profile/gas planning as I do.
If i were to dive say on a 100 foot wreck, where you are in a shipping lane, and have to return to the upline, I would almost certainly restrict myself to people with similar training.
If I am doing a days diving in the 70-80 foot range on catalina Island, I am much more open to diving with other people.
Each diver/team has to make their own judgement on which divers are "safe", which will follow their procedures "close enough" and for what kind of dives they are willing to dive with people with potentially dis-similar training