I have never heard of gunsmiths using CNC lathes. I suppose it's possible, but have never seen it. For gunsmithing I think I would want a 13x40 or 14x40 manual lathe. An older Taiwan made Jet gearhead would be a good choice. Many gunsmiths use the old 10x30 Clausing lathes. But if you want a 1 1/2 spindle bore you are going to have to go with at least a 13x40 with a D1-4 or larger spindle. Grizzly sells a ''gunsmithing'' lathe, but having used one I don't think much of them.
A friend of mine picked up a Jet 13x40 last year for about $1500.
If you really want a CNC lathe, then a CNC/manual machine something like this would be my choice. https://www.ebay.com/itm/16-5-x-40-U...UAAOSwQN1bCECb
In either case the accuracy is built into the machinist, not the machine. My old Jet 13x40 is repeatable to +/- 0.0001'', because I am. It's all about learning how and caring enough to do it.