How to prevent iphone switching off music from a Mac when using bluetooth?

Simply turning FaceTime calls off on your Mac mini—or on any other Apple device—may not solve the problem. This is because regular cellular phone calls received on your iPhone can also ring on your other Apple devices through Apple’s Continuity features.

For example, if a phone call comes to your iPhone and your Mac mini also rings, the music or other audio playing on the Mac may pause or stop. This happens because the Mac is configured to receive calls from the iPhone.

Apple’s Calls on Other Devices feature allows nearby Apple devices—such as a Mac, iPad, or another iPhone—that are signed in to the same Apple Account (Apple ID) to receive and answer cellular calls made to your iPhone.

If you do not want your iPhone calls to ring on your Mac mini:

1. On your iPhone, open the Phone app.
2. Tap Calls and then Call Settings / Calls on Other Devices (depending on your iOS version).
3. Look for the list of devices that are allowed to receive calls from your iPhone.
4. Turn off the Mac mini or any other device on which you do not want your iPhone calls to ring.

You do not need to disable FaceTime to achieve this. The important setting is Calls on Other Devices.

Once the Mac mini is disabled there, incoming cellular calls to your iPhone will continue to ring on the iPhone, but they will no longer ring on the Mac mini. This also prevents an incoming phone call from unnecessarily interrupting music or other audio playing on the Mac.

See the picture below for a visual guide to the setting.

I don't suppose you have calls on other devices turned on in settings?

If so, when the call comes in, it's coming to your phone and your Mac. the Mac stops the music to ring the call through and the music doesn't automatically re-start.

To follow up on KiltedTim's reply, see:

Make and receive phone calls on Mac, iPad, and Apple Vision Pro - Apple Support