Can I bring an unlocked Motorola Moto X Pure Edition XT1575 32GB (bought elsewhere) and just put my SIM card in it and use it on my Republic Wireless plan?
Yes, you can bring that phone.
As far as “put your SIM card in it”, if that SIM is currently in a Moto X1, X2, G1, G3, E1 or E2, then the answer is no. If it is one of the newer phones, then the answer is maybe.
If you have one of the older devices, you’ll need a new SIM. You can find them here: Bring your own phone to Republic! | Republic Wireless
In addition, please note that moving from an older Republic phone, to a newer BYOP phone WILL change your coverage and you should verify coverage here: Coverage Check | Republic Wireless
the Moto X Pure (XT-1575) is an approved 3.0 phone is needs to have a 3.0 plan and use a 3.0 SIM (a legacy phone SIM are CDMA SIM which are link to the phone and not your account)