Note that the scare tactc article doesn't even bother to quote a single line from the actual text of the bill. Churches hiring musicians will have no such difficulties, nor someone with some other business who does side work as a musician. A piano teacher working full time as a contractor through a teaching studio would be (and should be) classified as an employee with employee protections, but someone who only teaches out of a studio occasionally would still be independent. Articles such as the one linked are just scare tactics being used to drive opposition to a law that offer legitimate worker protections to employees who absolutely should have access to those protections.
A worker is an independent contractor under AB5 if:
* the worker is free from the control and direction of the hirer in connection with the performance of the work, both under the contract for the performance of such work and in fact
* the worker performs work that is outside the usual course of the hiring entity's business
* the worker is customarily engaged in an independently established trade, occupation, or business of the same nature as the work performed for the hiring entity