Do you have sympathy for the girls' anti-Putin protest in general?
I don't. Their "protest" was stupid.
I am globally not in sympathy with "all that avant-garde", although I visit contemporary exhibitions, concerts etc.
Last time I visited "King Crimson" concert - that was really unbelievable piece of art.
But pussies are kind of piece of crap.

Was it ok to break into this cathedral and stake a protest there?
I am not a believer, but it was absolutely abnormal.

Should the band members get punished by the law and if so, what type of punishment would you support? Or if they should not be punished, why not?
They should be arrested for 15 days. It is a kind of standard punishment for easy law-brakes in Russia.

What would have happened if somebody tried something equivalent in Brezhnev's time? Was this good or bad?
I am not sure, I was born in 1977, but most likely that person would be housed in a mental clinic for indefinite period of time.