County sheriffs are usually elected and don’t answer to local mayors, etc.
I believe you have hinted at a key vulnerability here. The County Sheriffs may refuse to enforce what they assess as an unconstitutional law. The local mayors and city councilmen cannot overrule them.
But "Police Chiefs are appointed, not elected". Those municipal and special district police organizations are going to do what the Mayor or City Councilmen tell them to do. If they don't, they will be replaced.
What are the directions the Mayors and Councilmen of various towns are going to give to their police departments? Have there been any statements of support for the Sheriffs?