I use my DS4 to play on my Mac sometimes, but when I connect it to the Mac via Bluetooth, my PS4 doesn't recognize it anymore, so I have to make the PS4 forget the controller only to set it up again afterwards. Is there a way I can make it so I can play on both my Mac and PS4 with the same controller (not at the same time) without having to forget/reconnect the controller every time I want to switch from one platform to another?
Ross' comment is correct. In the same sense that your phone can't be connected to two Bluetooth speakers at once, the same goes for the controllers. At least in the Windows world, I am able to connect my controller to my computer via a USB cable, while still retaining the Bluetooth connection to the PS4 itself. While I can't say the same for a Mac, I would imagine that it applies as well.
Of course, this is a non-wireless solution, and can restrict how far away you'd like to be from your Mac. If anything, Christmas is coming up, and if you celebrate it, it may be a good time to ask for a second controller if you'd really like to stay wireless.