That really depends on which police you're talking about, and one's views on the Constitution. State and local police have fairly broad powers, and I don't know much about California's laws, so I'm not in a position to judge this.

Why would they need a "legitimate reason"? They are people like any other people. Anyone has the right to read things on Twitter. Police officers are normal people, they don't have special rights or privileges and they don't have special restrictions or limitations. That is the foundation of policing by consent.

We are paying their salary. Why should they be spending time attempting to proactively police a group who is just exercising constitutionally protected right?

There is actual crime they could be investigating. Instead they are wasting resources on something that they shouldn't have anything to do with unless there is a threat of violence.