Wax is actually widely considered the lubricant for this application.
While it's an understandable concern, the small amount that may transfer to wood from incidental contact is a non-issue. Bear in mind the fact that planes, including smoothing planes which may be the last tool to touch a workpiece, often have their soles waxed. Some users even lubricate the soles of their planes with a liquid oil such as 3-in-One or a grease like tallow and with these too there doesn't appear to be any problem.
There's a good video on YouTube about clamp maintenance on Kings Fine Woodworking channel, showing how a good clean and waxing1 can transform the function of bar-type clamps; the title says it all, 83 - How to Clean Dried Glue from Parallel Clamps and make them slide Better Than New.
I want to mention that they also use a silicone lubricant to spray the internals on the moving clamp head, something I'm not sold on. Many woodworkers avoid all silicone lubricants in the workshop because of the persistent nature of silicone contamination1. Expect decent improvement on any sticky/grabby bar-type clamp if a normal oil or grease are used instead, if you too would prefer not to use a silicone lubricant.
Spoiler safety note: the testing in the video shows that acetone and MEK (methyl ethyl ketone) are both suitable solvents to help in cleaning off hardened yellow PVA glue residue. Acetone is significantly less toxic than MEK and is generally much cheaper too, making the choice between them easy IMO2 (they make the same recommendation).
1 Silicone is infamous for how it interferes with finish application (on new pieces and in refinishing) and in how difficult it is to get rid of every trace completely.
2 This isn't to say don't buy MEK at all (where it's still legal to buy retail....... sorry Californians, people in other places with a Nanny State), there are other applications where it is the ideal solvent choice. But take suitable safety precautions to protect yourself when using.