The guitarist has led opposition to farmers and politicians' efforts to combat bovine tuberculosis, and he submitted a petition with 234,000 signatures to Downing Street demanding the scheme be axed.
Speaking at the protest on the eve of the start of the cull in parts of Gloucestershire and Somerset, May said, "If the Government don't listen to us today the pressure will still be there.
"I think it would be easier for (Prime Minister) David Cameron to cancel it at this point, with some grace... I don't think there would be any shame in cancelling the policy because new evidence has come to light. It's not going to save money. I'm not the person who cares about money, I care about everything else.
"There is no scientific justification for it, there is no public backing for it, there's no moral grounds - but if it's not going to save the public money either then surely the foundations for this cull will disappear."
May has recorded an anti-cull anthem, titled The Badger Song, with Slash.