User/Developer can apply JSON formatting to one column and Field Customizer to another without issues.
If both JSON formatting and Field Customizer are applied to two columns in the same list view it will crash with something went wrong (see screenshot):

And while fixing this one, please, also check that list doesn't crash if for some reason user applied both JSON Formatting and Field Customize to the same column.
The bug has been fixed and should be available to customer in the next 2-3 weeks. Thank you for reporting the issue
@ahackettms awesome! Thanks for the update!
thx @ahackettms for confirming the status. Let's keep this open until we can confirm that things have been successfully fixed.
The fix has been rolled out and there's been feedback that this is still reproducing.
Closing the issue.
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Most helpful comment
The bug has been fixed and should be available to customer in the next 2-3 weeks. Thank you for reporting the issue