Does the Aussie media have issues with women in politics?

It seems the Australian print media has a vendetta against opinionated female politicians.  Palmer United Party Senator for Tasmania Jacqui Lambie has become the new woman to face criticisms.  She has spoken out against the burqa and Islam.  Now to clarify, the burqa is the full covering worn in various Middle Eastern cultures while the hijab is the head scarf which covers the hair and neck.  

Lambie has been told by various people to 'shut the **ck up' because she 'doesn't know what she's talking about'.  She's been berated by numerous media organisations, including Mamamia, News.com.au and now the Sydney Morning Herald has reported Queensland MP George Christensen has told her to shut up and that she's stupid.

Firstly Islam and Muslims are very controversial topics in Australia at this point in time particularly with the threat to Aussie citizens coming from IS extremists.  Australia defence personnel are in Syria supporting air strikes, but not yet participating.  There was the threat to the average Aussie last week that a beheading would take place in Martin Place. Fortunately ASIO thwarted that attempt.

Anyway, Lambie has copped a lot of flak for being anti Islam. By all means disagree with her but don't tell her to shut up.  Telling her to shut up is really un democratic.  Wouldn't it be better to say, okay Jacqui, I don't agree with you and here's why rather than telling her she's stupid!  Personally I don't think the burqa is even a problem but it should be banned simply because of the problems it could cause.  That's not what I want to discuss here though,  it's the utter disrespect for Lambie.  Does she need a new PR person? Yes most likely.  Should she shut up though? No.  She was elected to parliament and telling her to shut up goes against Aussie values of free speech which she is trying to protect.

My final question is: would she be copping this flak or be told to shut up and that she's stupid if she was a man?  Or is Australia still incapable of respecting women in politics?  The way Lambie is being treated is so reminiscent of the Gillard era.  Then there's the fact that telling someone to shut up for having an opinion different to yours is unAustralian, and Lambie wants to protect Aussie culture which we're lucky to live in and be a part of.