Imagine how differently Mass Effect would be if the war on terror did not happen?

If the WoT didn't happen, any Mass Effect might have been less military space shooter, yes. I think it was the 00s that really pushed that kind of concept hard. Not just Halo, and much more than the 90s did. Psst the aliens we shoot are code for generalized external enemy! That's not to say Mass Effect is actually all that stuff - its the liberal subversion to try to convince us to be more open and accepting - but the game mechanics and general genre design might have been less pew pew bad guys.

I do think there were seeds of things even as back as developing the first Mass Effect, that were dropped for what we got. ME1 seemed to work with a really corporate-themed skeleton, but then often ignored it for the dehumanized enemy faction and mutated or monstrous ('machine devil') main villains.

Instead, I do indeed think we'd have had more enemies that were associated with human and alien corporations, and the godly alien and/or machine overlords would be focused on managing us (with some exterminations) and not exterminating us (with some managing). The gunplay might focus more on the streets (like Citadel allies) than battlefields (Feros ruins). The conspiracies would be less about stopping or assisting the reaping of all life in the galaxy, and more about taking advantage of or assisting in the chaos of the struggle against our overlords.

MET has all the stuff I'm saying, but I think the focus might have been different. As the trilogy went on, SPECTRE mattered less, and N7 mattered more - military.