Redline's MT and MT-90 gear oils are formulated specifically for synchronized manual transmissions, which rely on friction between the synchro rings and the gears for proper operation. Somewhere on Redline's site, there is even a curve describing how the coefficient of friction changes with speed, which helps the synchro rings "grab". The difference in synchro operation is quite apparent when you switch.
But for a differential, a higher coefficient of friction just increases power loss and heat. Unless it's a limited slip, you want as 'slick' an oil as possible.
Hypoid gears (the ring & pinion in a normal differential) are particularly difficult to keep lubricated, because of the very high surface loading at the gear face (which literally produces a local deformation of the steel), and the wiping action caused by the gears not turning on the same axis. That's why they need "extreme pressure" (aka EP, aka "hypoid") oil.
And the Valvoline full synthetic GL5 works just fine, for half the cost of the MT-90.
I believe it actually works better than conventional GL4, by reducing heat (and power loss). There was a test report in Road & Track a few years (decades?) back, where they did head-to-head tests with conventional and synthetic oils. They actually measured about 7% more power at the rear wheels, just by switching to synthetic oil in the engine, transmission and differential. The power gain went away when they switched back. 7% may not seem like much, but that would be about 7hp behind a 100hp Triumph engine, and just a 2hp loss is about the equivalent of a portable electric heater. Imagine what one of those would do inside your differential!
Of course, if you only drive your TR in parades or on and off the trailer, then likely none of this matters. But some of us do drive hard on occasion, and even just accelerating away from a stop sign puts a lot of torque on the diff.