but if they act within the bounds of the rule of law protest should be against the movement or the system that allows this bad individual that does the bad thing

This is how it should be in a just world, but we do not live in one; it falls apart when you realise the rule of law is not a reflection of morality or ethics, and can be entirely corrupted by criminals with whom the rule of law only exists to use as a means of controlling and oppressing others.

I say fuck em. If you choose to be a politician, you should not be free from the consequences of your own actions, especially corruption. In fact, any corruption should land you in prison for life… but again, we do not live in a just world, and the only reason we even have basic human rights at all is because they were violently protested for, and 99% of the violence came from the state.