"Transphobic" is a made up word. So let's examine what those who use it mean;

Typically, those using it, take the word Transsexual ( being those who think they are able to be another sex by playing as that sex ), shorten it, to "trans". Then they add Phobic ( being an irrational fear of something ).
Hence they are trying to label others as having an irrational fear of those who proclaim themselves to be another sex.

We would point out the following:

• It's unkind to label others in an attempt to pigeon-hole them, and is in-fact a lazy bigotry. It lacks listening, empathy, and understanding. 
• There is a need to have rational discourse in any democracy. An attempt to use lazy labels to dismiss anyone's point of view is an attempt to shutdown the democratic process. This is a dangerous and slippery slope that leads to authoritarianism, also commonly known as fascism and dictatorship.

• To reduce legitimate concerns to irrational fear is as ridiculous as saying that because we are concerned about our children playing cricket on the motorway that we must have a phobia that needs mental health adjustment. It is disproportional and dishonest.
• There is nothing requiring that anyone accept another's delusions. Whether that delusion is of being able to change sex, or of being scared of another changing sex.

So we deny the label "transphobic". But we are very happy to be labelled as "concerned for our children".