Is it safe to mount a 65″ TV to the wall using 1 and 1/2 inch lag bolts instead of 2 and 1/2 inch lag bolts

Toggles and other heavy weight drywall anchors can be suitable for TV mounts when the mount is flush. Or toggles in to metal studs. Since the load is mostly shear and not pull-out, this is fairly safe. (Provided the drywall is thick enough, the anchors are installed correctly, the wall is properly supported, and lots of other considerations too numerous to go in to here.)

However, adjustable, articulating or arm mounts should never be used on just drywall or metal studs. No matter what anchor you use, drywall and metal studs can not handle the pull out force applied when a TV is extended or tilted away from the wall.

So either get a flush mount, or open the drywall and install appropriate wooden studs.

Measure the side to side of the back plate. I believe that most manufacturer's will have the plate long enough to span 2 wall studs. (BTW: most wall framing is established at 16 inches on center or 14 1/2 inches in between 2 wall studs). If your plat measures at least 16 inches install it on the 2 studs closest to the center of the wall. Some TV wall mounts have 3 axis' of adjustment: one axis allows you to swivel the TV side to side. This makes it easier to orient the TV on the center if the mounting plate was not. Also, it may be possible, depending on the mounting plate type, to offset the bracket that attaches to the back of the TV so that when it is hung on the wall mounting plate it is closer to room center.