I think Ennis and Jack don't fish on their trips because Ennis deliberately avoids fishing.
The "fishing buddies" tale popped out of nowhere when Alma asked how Ennis knew Jack, - and just there and then Ennis had a narrative safety buffer he seemed to need in compartmentalizing his married life from his love for Jack.
He has to tell his family *something*, however little, after those trips - and he evidently comes home spinning tales specifically about the fishing (based on what he told Alma after that trip when we *know* he didn't fish). In talking about fishing that never occurred, I think Ennis manages to limit the risk that anything of the real events and his real emotions, ever creep into what he tells Alma. He doesn't have to sift through his trips to tell censored half-truths, and everything real and true about his relationship with Jack remains all the more hidden safely away in his mind and heart and memory.
Otherwise I can't really see why Jack and Ennis wouldn't fish, being so close to running streams and having the fishing gear available. From the glimpses we get of their outings, there's focus on food and drink, and it's not like they spend all their time cuddling in the tent (more's the pity... ) ,and they did apparaently actually go hunting at one time. So realistically they would do some fishing unless they specifically decided not to.