Labels can been convenient, but they can be misleading. Editorial pages have limited space, broadcasters have limited time, and people have limited attention spans.
"Un-American", like the f-word, usually means whatever the speaker wants it to mean. Unlike the f-word, it always has negative connotations and is still used on TV. Taken literally, it means "not American" or "foreign". Use of the term implies that the speaker is closed-minded by dismissing certain ideas as foreign.
"Anti-government" seems to be another word for "anarchist". It's not a fair term to describe those of us who acknowledge a role for government. Those who advocate dissolving all national, state, and local governments either don't understand what the consequences would be, or have a completely different value system than the rest of us.
So the next time you hear "un-American" or "anti-government", take what that person says with a grain of salt.