To be honest, I don't understand why the police even vaguely tolerates the concept of a counter protest. If they consider it within their job to make sure protests don't turn violent and disperse them if they do, why allow a group to yell insults right at people's faces?

What do they think is going to happen? Hugs? Pepsi?

No; if a group has dutifully informed the police of their intent to protest, and gotten whatever authorization is required, then any other group trying approach them to protest them should be very forcefully dispersed. Anything else is inevitably going to lead to violence.