I might be OK with it if they _both_ asked me to do it because it has to be a third party doing it for some technicality. But it would sure feel weird, and I would worry that down the road I might be blamed if things became less amicable...
If they both want it done I'd say half jokingly "only if you pay my bar tab." Then I'd serve the papers and enjoy my free drinks. If there is any animosity I'd say no and run like hell.
You have the weirdest friend situations. I have to think there is a common thread. Like most of your crazy situation posts, the answer here is just don't get involved in their business.
Do not pass go. Do not collect $200. Do not rationalize getting involved because Person A said this, Person B feels that way, etc.
I don't know California law at all, but even assuming there was a law requiring service by a third party, I don't know why they wouldn't just agree to waive formalities.
If waiver isn't available in your jurisdiction, and both parties are *really* okay with it, I'd do the service. No reason to make things more difficult for them by refusing.