We have a constitutional right to freedom of speech, the right to peaceably assemble, and the right to petition for a redress of grievances. Taken together, these add up to a rather sweeping right to protest. BUT: we do not have a right to harass others, to disrupt other people's events, or to interfere with them as they go about their normal activities.
The protest culture in America jumped these limits long ago. This probably started with the labor movement and picket lines. It escalated with the civil rights movement and, a short generation later, the antiwar movement. The left today spends a LOT of its time on aggressive, disruptive and harassing forms of protest.
It is utterly revealing (but hardly surprising) that the left now finds the protection of abortion a cause for which it will recognize a limit to protest.
That said, I'm generally ok with some, not all, of the types of restrictions on demonstrations being proposed in this legislation -- as long as they are applied equally to all forms of protest against all targets. No double standards. Protestors should not be allowed to block entrances or harass people coming and going. Speaking to someone quietly and respectfully, however, is not harassment. Nor is offering a pamphlet. These lines must be drawn carefully. Antiabortion protestors have exactly the same rights as do union members on picket lines or leftist demonstrators on a college campus who want to protest a speaker.