I guess it would mainly depend on what it is, but the crux of most conspiracy theories is basically a proposition that politicians or government officials might be lying about things. People who mock or cavalierly dismiss conspiracy theories out of hand are as much as claiming that "politicians never lie."
Another thing I've noticed is that many people are quick to believe any conspiracy theory about other governments (particularly about the SU during the Cold War), yet concurrently believed that our government could do no wrong.
On the other hand, there's something almost defeatist about conspiracy theories, since they make the government seem soooooo powerful, as if no mere mortals could ever hope to oppose them and survive. Conspiracy theories strike fear into the hoi polloi and keep them in line.
For me personally, I don't actually believe most conspiracy theories (although some theories about JFK are intriguing). However, I don't really care that much about them either, and I can't understand why anyone else would.
The only exception I would make would be the anti-vaxxers, since that kind of talk can harm people.
But I have no cause to defend the government's reputation if someone accuses them of hiding aliens or assassinating presidents or faking the moon landings. It's no skin off me either way, and it doesn't really hurt anybody. The worst that might happen is that people might lose faith in the government, or they might be more skeptical when it comes to claims made by the government.
It makes the government seem smart IMO. Evil but smart. I don't believe they are that smart.