When I do outreach events, I make sure that there are at least two other adults in the room if there are kids present. When I have to interact with kids at public events I make sure to address the parents before talking to the kid.
Read the Scouts Rules here if you want.
Sure, it's a problem, but his diagnosis seems off the mark:
I'd suggest the problem in the UK has more to do with (1) tabloids stoking paedophile paranoia for decades (blowing up each case into a fear that paedophiles lurked in every neighbourhood just waiting to prey on your kids), and (2) the discovery of a systematic cover-up of paedophiles in prominent positions in UK society (Jimmy Savile, other entertainers, several politicians from the 1960s to the 1980s at least, the Rotherham scandal, etc.). And we don't seem to be done with number 2 yet.
So let's not blame feminism for this. The slogan about potential rapists is one I haven't heard for about 30 years so I doubt it's highly influential today. And a rapist is not a paedophile so the connection doesn't really make sense anyway. The paranoia about paedophiles comes from other sources.