Should I use oil or polyurethane to protect new cane chairs?
Interesting question... 


I'd never think to use scotchgard. It might work, but if it doesnt, any finish you try to apply on top will not stick. Maybe try this in a hidden area to see if it provides protection. 
Tung oil can be a mixed bag - there's a difference between the pure stuff, the tung oil + driers, and the tung oil "finishes." So if you buy the wrong thing you could get either a nice gummy mess that takes forever to harden, or plain up thinned polyurethane. 
I would recommend using thinned polyurethane or a "wiping varnish" - this can be purchased diluted, or you can buy poly and dilute it yourself with mineral spirits/Floetrol depending on if it's oil or water based (respectively). The advantage of thinning it is that it allows you to get more working time to evenly coat all the nooks and crannies, and it builds thickness much slower, preventing the wicker from looking plasticy.


Both tung oil (any version of it) and oil-based poly will darken slightly with time, turning a light yellow. Water based poly will not darken as it ages, but is not quite as hard... probably a good thing for wicker.

Ultimately, I'll recommend the thinned, water based poly.