SRAM 1:1 shifter + Shimano 11 speed MTB RD
 

I'm planning my next bike build with an 11-50 cassette but I don't want more than 10 gears for personal preferences. I've seen Chinese-brand drivetrains (LTWOO) that can do this but I want something a little more robust. I figured from looking up on articles and discussions about pull ratios that a 10 speed 1:1 SRAM shifter could work with Deore RD-M5100-SGS but I'm not very sure. Are these compatible? Or is there something I missed?

Why not just get a SRAM derailleur that works with the setup (1:1 is generally 9 speed and below) or get the correct Shimano shifter which makes more sense.

No idea now why you would want such a massive range and fewer gears that is just silly. The whole point of having that range is also having more gears so more consistent gaps between them for better smoother shifting. However regardless get a full Deore set up or a full SRAM set up and be done with it. No need to do some odd mixing and matching that won't really work as well or at all depending on the parts chosen.

If you are looking to save money and get a low cost groupset Microshift Advent X would set you up well. It is a decent set up it is 11-48 but that is damn close enough and considering you can get integrated road/gravel shifter/brake levers as well it is pretty awesome for a Tomac style bike or a gravel set up as well as standard trigger shifters for mountain biking.

There is no 10 speed SRAM 1:1 that I know of.

SRAM 1:1 was 8-9 speed. It's is very close or the same pull ratio as 11-12 speed branded X-Actuation and Shimano 10+ speed branded Dyna-Sys, as long as you match the cassette speeds to the shifter speeds. I set up an 11 speed bike for my wife with a SRAM RD but my wife hated the shifter and I just changed it to an SLX and it was fine.

But SRAM 10 speed specifically alone was the same pull ratio as their road groups, branded Exact Actuation. You can see this for example when you compare an 11 speed Apex to 11 speed NX RD. They are almost the same except for that bit that sets the leverage.

I'm running Advent X with no issues. Advent X uses 1:1 so one hack you can do is run a shimano deore 5100 11 speed RD. The Advent x RD may clear a 50t cog but the 5100 is made to go to 51 so it for sure will.