They are allowed to live a normal life, so long as they don't publicly disclose classified information
Stargate Atlantis Season 3, Episode 10 "The Return, Part 1" involved a ship of living Ancients being discovered (who wanted their city back) and the Atlantis Expedition returning to Earth. While some of the members indicate that they will now be working with the SGC or Area 51, others have alternative options.
Zelenka considers a position at a public university in the Czech Republic.
Zelenka: Well, I was offered a position at Masaryk University right before I came here. I imagine I could work there if I wanted to.
Weir can work with any government she chooses.
Sheppard: Every government in the world's going to offer you a job.
We know from Season 6's "Disclosure" that the American, Russian, Chinese, British, and French governments know about the Stargate program, but I see no evidence that every government in the world knows about it. Weir does have accomplishments aside from the Stargate program (indeed, she only found out about it during the SG-1 Season 7 finale), so it's quite possible that she would be valued even if her experience with Atlantis is not known.
Later, Carson goes to visit Weir, who it turns out has not taken any job. She has been writing, but it's clear from Carson's reaction that she can't publish her memoirs since that would be sharing classified information.
Beckett: How about you?
Weir: Oh, you know. Keeping busy.
Beckett: Oh, yeah? Doing what?
Weir: I've been doing a bit of writing, uh, working on my memoirs.
Beckett: Your memoirs? About your time in Atlantis?
Weir: Yeah, somewhat.
Beckett: And on what planet did you expect to publish it?
Weir: I suppose it's for posterity as much as anything else…and for me.
Note that in the real world, civilian contractors are granted classified access all the time. I strongly suspect that disclosing information about the Stargate program would fall under 18 U.S. Code § 798 - Disclosure of classified information, or an IOA equivalent, which says that any person disclosing such classified information
Shall be fined under this title [currently up to $250,000] or imprisoned not more than ten years, or both.
A 10 year prison sentence and $250,000 fine is a pretty good deterrent for most people to not reveal the presence of the Stargate program. That said, there are some who would consider violating that anyway, like Senator Armstrong's wife (a non-government civilian) in Stargate Universe's "Air, Part 3".
Mrs. Armstrong: You tell your superiors, if anything happens to her, I will go public with what I know. [...] My husband gave his life for my daughter. You get her back to me. Or the whole world is going to know what has really been going on these past years.
However even if a leak did come out, Stargate Command has plenty of plausible deniability including a cable TV show and advanced holographic technology projecting little gray men.
And after the events of Stargate SG-1's "The Road Not Taken", I imagine that anyone thinking about disclosing the Stargate program would be required to read Samantha Carter's mission report describing how bad a parallel universe was in which the Stargate program was revealed.