A few things:
1) If you haven't already done so, copy the "config" folder from the MiSTercade Github over the top of the "config" folder of your MiSTer's SD card. That should update all the MiSTer core mappings to match the MiSTercade hardware.
https://github.com/misteraddons/MiSTercade-Config
2) There's also a script you can copy to your SD card and configure that will update your MiSTercade control bindings whenever the "update_all" script is executed. This will keep your MiSTercade bindings in sync with new cores as they're released.
https://github.com/misteraddons/mistercade_mappings
3) If you still need to rebind your controls after updating the MiSTercade input scripts, you'll want to disable the P1 Free and P2 Free switches that triggers Coin and Start simultaneously whenever you're assigning button mappings or else you won't be able to bind the Coin and Start inputs properly. You can re-enable the switches after. Press the Coin button on the MiSTercade Remote or physically insert a coin into your cab to trigger the Coin binding.
4) When binding controls you can skip a unneeded binding (such as Pause or Credits) by pressing the User button on the MiSTercade.
NOTE that the "Credits" control binding on some of the cores toggles display of the developer credits - it's a completely different (and skippable) binding than the essential "Coin" input that triggers inserting a coin into the cabinet.
5) Also note that many arcade games allow you to enable Freeplay in the Service Menu if you want to leave the P1 Free and P2 Free switches on your MiSTercade off.