Well, I'm a player in Age of Ashes, so have purposefully avoided reading the modules, so can't really comment on specifics. But IMHO you should always modify APs to suit your needs and your players. Why?
1) APs almost invariably have a very strong element of railroading. You expect to go from page 35 to page 36 to page 37, with little margin for variation. That kind of stuff may be fine for some folks, but my players are constantly coming up with crazy ideas that are not covered by the adventure as written - NPCs they want to interact with, locations they want to take a look at, even plot points that they have imagined, but that don't actually exist in the module as written. But who's to say they're wrong? If the PCs are pursuing some alternate location, plot point or NPC interaction, why not simply roll with it?
2) Your players all have unique characters, with their own story that was not envisioned by the writers of the AP. Adapting your story to include elements from your players' backstories, or even inventing backstory-ish elements that you project on your players, helps them reach that happy state of immersion where they feel like the adventure is (at least to some degree) really happening to them. It's not easy to pull off, but when you can do this, it's roleplaying GOLD.
3) I often find that the motivations ascribed to NPCs and even monsters are shallow and lacking in interest. So many seem to be programmed to fight to the death. Sure, maybe it's quicker and easier to write the adventures that way, but it often feels better to me to have adversaries adopt less than optimal tactics. Maybe they take an action or two to realize what's happening. Maybe they waste an action here or there to gloat. Or even monologue. Maybe some of them try to save their skins rather than fighting to the death.
4) As a corollary to 3, I often try to "fudge" combats, especially if I am forewarned that it's super deadly and risks a TPK. I don't fuge die rolls (all my dice are rolled in the open, except for PF2's new concept of secret checks) but I often add in things that change the dynamics of a conflict. For example, if there's a super deadly trap down ahead a ways, maybe a minor adversary from a previous fight will get himself chased down into that trap, activating it instead of the PCs. Or maybe the PCs will encounter a non-hostile NPC who will tag along with the group long enough to become a red shirt, dying in a dramatic way that emphasizes the danger without requiring a PC die instead. Or maybe the bad guys are sleeping on the job, or otherwise distracted from their mission of killing the PCs, like the goblins in RotRL who were busy fighting over pickle jars or torturing seagulls.
All these things enhance a group's experience with a pre-written adventure. I don't see how your players could really complain about you, the DM, stretching your creative muscles to make things more interesting for them. Don't let yourself get locked into the railroad of an AP. Make the story your own by adding and subtracting liberally along the way. The only real risk you run is having the players go completely off the reservation, into non-AP-oriented adventures that you have to make up on the fly, or between sessions. This is good. Go with the flow.
