Nothing wrong with wider tires, like 32mm, but there's also no problem using 23mm ones on this route. That's what I've had the last few times when riding with full camping gear. The road surface is generally pretty good so use whatever tire width you usually find comfortable for a long ride.

In addition to a driver's license or similar ID, Pendleton generally also requires use of a helmet. And they do sometimes close the base to cyclists (right now through the weekend is one example). The shoulder of I-5 is always an available alternate - but going through the base is nicer.