Cyberpunk 2077: Phantom Liberty is a preem spy thriller adventure. However, if your V really isn't that interested in working with government types, you can choose not to sign on to a life of martinis shaken, not stirred.
Only issue is, choosing to do so locks you out of the questline—and from what I've tested, it's permanent. At minimum it'll delay your progression through the DLC's story substantially, but I don't get the sense Reed's gonna call me back.
Here's the mostly spoiler-free rundown: at the end of a mission called Lucretia My Reflection, you'll be given a choice to stay or go. If you go, you really do go—you fail the mission, and are roadblocked from proceeding.
You can still run around Dogtown, but there'll be no suit and tie galas with Mr. Elba, which is a crime in itself. Just make sure to play ball with your new friends, and you'll be golden. If you're really worried about accidentally dropping the new DLC, here's the specifics.
Lucretia My Reflection is the fourth mission in the DLC's main questline, a couple of hours into the DLC's fairly opening gauntlet. The missions before it are, in order, Dog Eat Dog, Hole in the Sky, and Spider and Fly.
To save you the anxiety of accidentally flipping off the FIA, you'll want to start paying attention when Reed reunites with NUSA President Rosalind Myers. While the two stand in front of a gloomily lit, blinded window (in true pulp noir fashion), you'll be given a choice to say "You're right, I'm out".
This isn't immediately binding, and the game gives you a chance to stick with the plan. President Myers warns you "Walk out of here, and the deal's null and void—understand?" If you select the option "Made my decision", you'll fail the quest completely and be left feeling sorry for yourself on the streets of Dogtown.
You'll immediately fail the quest, and have no way to progress through the DLC's main story. Reed will contact you a few days later to let you know the President made it out safe and sound, but he'll then immediately ghost you by deleting his account. No hard feelings, then.
Getting the choice to just persist in a DLC-less world is pretty funny, though a major pain if it's been a while since your last save. I can only assume this choice is here for diehard roleplayers who would deny themselves Mr. Elba's star-studded company, all to avoid cosying up to the feds. That or it's just a useful choice for new playthroughs, where you might want access to Dogtown without doing the whole Phantom Liberty questline all over again.