Is it against the rules to push two side by side tables of four together to seat a party of seven, or is better to make them wait for 30 minutes until one six top is ready?

It has a great deal to do with fire codes. I hope it was worth the wait

Sometimes particular table configurations can't be moved because of fire code. Or the tables might split multiple server sections. As a former waiter, I can tell you that the staff are likely as frustrated as you are. I always was.

Apparently the staff here has no clue

You can push tables together.