I don't really see how being rendered effectively extinct as a civilisation and race (in their eyes) is going to endear the wastelanders to any remaining Enclave personnel. Like seriously, people think of the Enclave like the Brotherhood when they aren't. The Enclave considers themselves a sovereign nation, the United States of America, that they are working to restore and of themselves as a separate race to literally everyone else.
If something came along and destroyed your entire way of life do you really think that would soften your edges? Particularly when it was done by the very people you were told were the enemy (aka everyone outside of the Enclave).
It really wasn't like that at-all. They are obviously lying to you if you've played Fallout 2. Enclave patrols literally quote a law which obliges them to kill you and they certainly don't act sad about it.
Presumably they know admitting their compliance and support of mass genocide, purely done to make their lives easier, isn't going to win them any friends. Hell if they "were" being sincere, which I don't believe that they were it actually makes the remnants looks like completely amoral sociopaths rather than good people.
The Project, you know the genocidal plan to exterminate everyone else, was not a secret but was in-fact considered to be their "salvation". Judah Kreger saying "The leadership was ruthless but we just wanted to civilise things" is a lie, straight-up.