I finished "Old Wounds" and see that the next mission is "Time and Fate" but I'm forced into "FOB Spectre," a strike force mission. I'd like to finish my Veteran run without doing these strike force side-missions. Is there a way to bypass them and get back to the campaign?
Not directly that I am aware of. They are quite quick to bypass, since you only get a certain number of tries based on the number of campaigns you completed. I failed 3 times completing mine, and then ran out of "credit" but from then on forward you don't have to do them at all even if you have credit since the rest of the campaign doesn't include any.
It seems that the idea is that the FOB Spectra has to be played once as part of a campaign run through. I am guessing the purposes is to introduce everyone to the format and make players aware of it's existence.
I did try various ways to skip doing the one but it seems that you have to try it at a minimum once.