will left wing progressives who love Gaza really have that big of an influence

Labor have dropped the ball on a few of their assumed voter bases, people concerned about Gaza/Lebanon/etc. is one and another sizable group will be unionists. The dodgy CFMEU administration has taken many Labor voters in my union by surprise, and in at least some of their rallies the speakers have called for voting for further-left parties, suggesting the Greens as an example.

Looking at NSW and Victoria council election results, I expect the Greens will gain votes and maybe even a seat or two, I doubt there will be drastic gains or losses.