Okay so does the sony RM-1251 crt projector use the same remote as the Sony RM-1271 CRT ?

yes

The "RM-1251" is the remote. As is the "RM-1271" and many other "RM-xxxx" remotes. The projector is actually called a VPH-1251. And yes they all interchange. Some may not have all the features as the bigger remotes but what it does have will work.

There are several RM-xxxx remotes that work. You want the big one, not the small one. The RM-1270 or RM-1271 I know works. I think there is a lter version that came out for the VPH1292 that has an additional button, but still works for the non-1292 VPH-12xx units. Watch out for the numbers - there is a large RM-1270, and a small RM-1270s.