T-Mobile and Verizon should allow any modern device. Verizon used to need a activation conponent for the CDMA radio but modern devices just use LTE and voLTE. They did have a visual voicemail blob that used to be pulled in, but now they follow spec and don't require anything special.
Sprint (which is now T-Mobile) has required an activation app for their CDMA devices called SprintDM. Without it, phone will not activate and work. Most alternative OS like LineageOS don't include it, but if you activate on stock OS and don't wipe modem partitions, it continues to work. Thankfully they are transitioning to T-Mobile network.
AT&T has no activation crap but may not let imported devices based on IMEI numbers they don't have.