No, it's not fascist. What the anti-monarchists failed to mention is that the protestors were not arrested because they were protesting, they were arrested under suspicion of attempting to lock-on[1] but were later released without charges because of a lack of evidence. There is a debate to be had about what a peaceful protest is but frequently people use the right to disrupt other people's lives such as blocking roads. I don't think there should be a human right that can deny other people the right to use public roads and paths. That would deny others the right to protest peacefully also.

[1]: https://en.wikipedia.org/wiki/Lock-on_(protest_tactic)