Should be fine. I run Force 1 with 10sp. Zero issues.

sram told me not to try running that clutch RD with a 2x. They said it won’t work well.

Not that you asked, but I’ve had good experiences running an 11-36 with the sram WiFli etap RD. You just need to make sure your chain is the right length and the b-limit screw is set so that the pulley clears the 36t on the cassette.

Unfortunately I don't think etap is in my budget.

I've also heard of people using a 10 speed MTB derailleur that has a larger range.

I'd probably opt for an Apex wifli rear derailleur ($50 brand new). Designed to work with 2x 10 speed and with the b screw adjustment can likely work with a 36t. Just can't cross chain.

Are we to assume you currently have SRAM 2x10?

No way a Rival 1 "short cage" has enough chain wrap. Not sure if the "long cage" would or not, but the 1x specific X-Horizon geometry probably means you have junky rear shifting in one or the other front rings even if it does. And the clutch probably makes the small->big ring shift a cludge.

That said, any of the long cage SRAM 2x10 speed mountain bike rear derailleurs would work with SRAM 10 (or 11) speed road shifters. For a one-off use, the ~$40 X5 will do the job just fine.

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"They're made of latex, not nitroglycerin"

Do you run it with a FD, though?

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"They're made of latex, not nitroglycerin"

I would buy a new crankset with 50x34 chainrings.

yes, rival 2x10 with medium cage rear derailleur that maxes out at a 32T cog.

My older frame (08' Cervelo Soloist Team) won't allow the front derailleur to travel low enough to work with a 34T front ring, tried that already. So I've got to get it done on the back.

Sounds like the MTB rear is the way to go. Or sell one of the kids and get a new bike. Tough call...

Not currently, but I have. I was using SRAM 10sp R2C TT shifters and a Dura-Ace 7900 front mech.

Srams 1x derailleurs are not meant for use with a front derailleur.

So apparently though I said it was fine for me, the 1x RDs are not designed to pick up the chain slack from a ring shift. I didn't notice it. But that sounds pretty valid......

They can pick up chain slack just fine. The problems are that the clutches make for more drag on a front upshift, and that their geometry doesn't guarantee good rear shifting when the front shifting is messing with the cage angle. Sometimes it probably "just works", as is how drivetrain stuff goes, but there's a reason that basically all modern 2x/3x front derailleurs use a slanted parallelogram.

I used to run SRAM XX 10-speed MTB rear derailleur with SRAM Red road shifter and SRAM 11-36 cassette without any issue. I now run the same rear derailleur with SRAM Red 22 road right shifter (11-speed) and Shimano XTR 11-40 cassette. Again, no issues.