I had exactly this issue: Mazda radar control error below 20mph and auto-hold not engaging after a remote start (after market, I think it's a compustar brand), everything works fine if started manually. As I spotted right after the remote starter was installed I was pestering my installer for a fix, which in turn pestered the manufacturer of the remote installer. The remote start manufacturer just released a new firmware, I got it installed today, and I'm happy to report that everything works perfect now: Remote start, unlock the door, open door, engine still running, take over by pressing brake pedal, and drive out as usual with all systems working as expected. Get in contact with your installers and hey could perhaps get it sorted.
Which one did you have installed?