I think the critical part of that question is how you define goverment.
If you believe governments are ligitimate non-corrupt institutions that are representative of the people and have the citizens - and all the citizens - best interests at heart, then you will likely think banning "bad" ideologies is a good idea. If your thoughts towards government move in more negative directions i.e. you cannot trust the government's moral judgements of right and wrong - you'll likely be against the general case of banning ideas.
Historically speaking governments seem to do very poorly at separating good ideologies from bad ones - i.e. Nazis entartete Kunst, various banned books such as Animal Farm in the USSR. A scroll down the list of banned books (https://en.wikipedia.org/wiki/List_of_books_banned_by_govern...) reveals this fact.
I'm sure there are other interesting pros/cons to this question, anyone else care to give a try?