Where we fish in JDF in the summer for big Chinook with a full moon/big tide and the related strong current, we have found that being ready for the short secondary bite times during mid-dayish tide changes is critical. With the current ripping they are often not feeding and may be hiding out deep or in the lee of structure, waiting for the current to slow down and then feed heavily for 20 minutes or so on the tide change. Make sure you are on one of your good proven spots for the change and your gear is weed free, and the chovies etc. are working. Have replacements ready and pre-rigged to snap on and work the gear quickly. That is often the difference between one big salmon in the boat and several.
As to the decision to fish or not, the wind/sea state is a much bigger factor in the decision for us, than full moons. It is just more fun and comfortable not to mention safer and we don't want to be out their fishing in the bumpy water unless we already paid for Derby tickets, especially if the wind is pushing against strong current.