May I add one thing?

What I like about McDonald's is that the fry area is the fry area and the
burgers are over there and the nuggets are over there.  Meaning: each food
seems to have its own station and only fries are cooked in the fry oil (from
what I have seen).  Nuggets are not cooked in the oil that fries are.  To
me, that reduces a lot of the risk and McD's is top of our (now very
infrequent) treat places to go.

As for pizzas, you could ask for a cheeseless pizza but still find cheese in
the sauce or even milk in the dough.  A homemade dough recipe that I
modified for my own use originally calls for milk.  But I made the dough,
found a pepperoni without dairy and made my son a cheeseless pizza (soy
cheese is terribly expensive and often contains casein) and he was so, so,
so happy!  And the dough was fantasic.

PS: Avoid doughnuts.  They contain milk too but if you have a deep fryer and
know how to modify a recipe, you can make them at home.  They were fatty &
greasy but amazing.

Good luck!