I've been spending a lot of time on my shortboards for the last year or so - so much so that when I did recently get my sup out for a surf, I really noticed how out of touch I was with my sup surfing skills. Going back to a short board, you do really notice how annoying it can be when a sup (or a longboard - equally as bad / if not worse) is also at the break. I think that the main thing is to be mindful of the conditions, and what people can and can't catch on their respective craft. A sup can have fun on waves that a shortboard can't - not saying you should always deny yourself of a good wave for giving it to shortboarders, but if you start to take all the good waves and only leave the crap ones for them, you're not going to be popular (which would be the same regardless if you were all on the same craft).
I haven't spent much time at Cronulla but it's a pretty big beach. In the last couple of times I've been out on my sup, I've tended to paddle the beach, catching a wave at one break and then paddling up to the next one, catch a wave, move along. I've been doing this mainly because I want to get my paddling endurance back up a bit, but I think it has the added benefit that you don't end up dominating a break. I'm up at Dee Why which is a shorter beach than Cronulla, but imagine that you could be spoilt for choice of waves down there if you paddle around a bit.
I know that it may not be fair to have to curtail your selection of waves, but if the aggression is grinding you I think it's generally worth it to act in a manner that minimises the chances of that happening. As someone who spends their working life arguing, it's not worth bring that in to your play time.