A neutral position would accept all parties.
Don't want to take a position on religion? You accept advertising from Muslim, Baptist, Catholic, Atheist, Agnostic, Satanist, etc.
Alcohol? You accept advertising from Budweiser and Mothers Against Drunk Driving
Guns? Advertising from Ruger and the Brady Campaign.
THAT is "not taking a position".
Accept advertising from atheists and not Baptists? The Brady Bunch and not Remington?
That's not neutral.
Still happily answering to the call-sign Peetza.
The problem, as you so eloquently put it, is choice.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.