I've looked around for any other conflict reports between these two popular mods, but haven't found any (not one).

UFO was working perfectly until I installed Requiem. Now the UFO MCM menu is broken (follower's names don't appear there), I can't hire more than one follower, and a lot of the dialog is missing.

I've tried adjusting the load order, but that had no effect.
Any help is appreciated.

I am running the older version 1.2i together with Requiem without problems. UFO should be after Requiem. The newer versions are different though, but as you said, there seem to be no reports that they don't work together.

You should also post your question on the Requiem page on the Nexus, I usually get quick answers there.

I'm running UFO 1.2j...

I had UFO loaded before Requiem when I hired Belrand, I noticed his name didn't show up in the MCM UFO menu, so I moved UFO to load after Requiem and tried again. His name still didn't show. I kept playing anyway, and tried to hire Marcurio later.... he takes the money, but then stays in the Bee and Barb. All his dialog except "What are you good at?" and "You know..." are gone, and "You know..." simply leads to "Never mind".

I looked at "show playerfollowercount" in the console before and after trying to hire Marcurio, it says 1 both times... so he isn't even registering as a follower.

I fired Belrand, then immediately re-hired him. Now he DOES show up in the MCM UFO menu, but I still can't hire Marcurio. (These are my 2 favorite followers, so I'm sad... very sad.)

I'm still in Riften right now, but as soon as I get back in the game, I'll go somewhere and try to hire someone else. I'll report the results...

Edit:

I've posted my question on both the UFO and Requiem mod pages on the Nexus... I'll post any solution I get (if any) from there here.