For clarity, airlines will typically do two background checks.

One is the SIDA, which is required by law for 121 crew, period. Some crew get a SIDA badge at their domicile, but most do not these days. Probably the only places that still do that use the SIDA badge to open the gate to the parking lot, or some other logistical access reason. But you get the check regardless of whether or not you get a badge. And if you ever get convicted of a SIDA crime, you're unemployed.

The other is whatever additional HR checks they want (and are allowed by local law) to conduct. Something which is not on the SIDA list could be no-go here, ex, possession of kiddy porn, domestic violence, heroin possession. Some regionals today may only do the required SIDA check, ie they cannot afford to be picky... so you could have a felony and be an airline pilot as long as it's the right felony, and FAA aeromedical gave you a pass on your medical.