I don't have faith in government. Government is merely a necessary part of the equation. In the eyes of some, this makes me a conservative. Conserving what? I think taxes are necessary, that social programs can do good (including forms of welfare), that no one should be discriminated against, and that the God of the Bible does not exist. Somehow that's not enough because I don't subscribe to the theology of government.
Seriously, I don't know why you think lacking faith in government is a good metric for guessing whether someone is a conservative, as if it even matters for such a comment. Do you assume someone is Black because they say they like basketball?