Can I buy an unlocked MOTO X Pure and activate it with my Republic account?
Yes but not from Republic and maybe not new. The Moto X Pure is a 2015 phone, so finding new ones is likely to be increasingly difficult. In any event, if the Moto X Pure is your choice, please be certain to acquire model XT1575.
If a newer phone might appeal to you, some information from fellow community members may help: How to Find a Compatible Unlocked Phone.