I've made this same argument with atheism. Shrill voices on one side are an essential part of the movement. If the most radical thing you hear is a moderate, rational view and the most reactionary thing you hear is "barefoot and pregnant" the result is most often an opinion between moderate and reactionary. By hearing the extreme radical view the result changes to the center by showing that the moderate view isn't as radical as it would otherwise appear.

This has been shown to be successful and is the tactic that Fox news has used since its inception. Be way to the right, thus drive general opinion to the right. It is also a basic tactic of negotiation - you always ask for more then you are likely to get because you know you'll have to trade something away. A friend of mine who is into game theory told me that generally the best strategy is tit-for-tat. Escalate a response equal in scale to your opponent. IMO, liberals in the US generally aren't doing this well and that is why they are losing.

Pizzey apparently wants to be one of the moderate voices which is fine because they serve a purpose as well, by coming in behind the radicals and discussing the moderate view. In that sense the militant feminists will make her life easier. She should be thanking them for that.