Okay, throwing a spanner in the works here - what nationality are these families that are throwing the party? I'm asking because:
1) If English is not their first language then they could easily stuff up the wording of their invitation
2) The concept of "bring a plate" is a very Australian/New Zealand thing. No one else in the world (that I know of) does it, so it could be that these people are a bit confused as to how it works and don't want to offend the "locals" by not giving them the option of bringing their own food, if that makes any sense...
I know that when my family first moved to New Zealand we were very confused by the "bring a plate" thing.

Even if the families are not from foreign countires, I still don't its rude to ask to bring a plate. I read it as an "option", e.g. if your child has allergies, is fussy, or something, then they can still have something to eat and share with their friends, rather than not eating anything... JMO. Also, I'm sure everyone would still be happy for you to come and join in even if you don't bring any food.