At this point screw the fallout from the police union. Rip it up and renegotiate if the existing contractual obligations are too restricting. Realistically whatever recourse the union might have for breach of contract would be worth it. The most damaging action they could take would be to strike, and if they did public support would be against the police at this point and that would be a boon to appeasing the protesters. Heck, make it a PR stunt and start a campaign to get protesters to enroll in the police academy and fix the injustices they're marching for.
Either the PD gets replaced wholesale and the union can pound sand and the protesters are appeased or the union comes back to the table to come up with a reasonable deal that lets the municipality make some real changes to appease the protesters. Regardless of how they proceed serious accountability is crucial.