Bigoted? Maybe. Ignorant? Maybe not.
"But her position is ignorant and bigoted because it takes an idea to turn someone to terror and it's now impossible to stop the flow of ideas."
Her position is that by stopping all Muslims from entering Australia, we can stop the (say) 2% of Muslims who are potential terrorists. It doesn't stop Muslims already living here from becoming radicalised, but if there is a percentage of the Muslim population prone to becoming Terrorists then stopping the Australian Muslim population growing does seem a logical way to put a lid on future growth in this area, as well as making it difficult for ISIS and AL Qaeda to infiltrate sleeper agents into our country. So it might be bigoted but it isn't necessarily ignorant, as it is based on logic, and it seems as if we have no way at present of distinguishing between good (as in safe) Muslims and Bad (as in psychopathic religious fanatics with serial killer ambitions).
I could also add that it takes more than "an idea to turn someone to terror" - they have to be ready for that idea to kick off their psycho-killer predisposition. I could argue that it is too possible to stop the flow of ideas: the Government could block all internet sites from terrorist organisations, and force Facebook to close any account that uses certain key words such as "Kill the infidels!" I'm not saying this would necessarily be a good thing, but it could be done, with the political will to do so.
A bigot is "a person who is intolerant towards those holding different opinions." There goes all the Labor Party and the Greens, then: they are bigots towards non-socialists!