I get that might be the case for the training, but as soon as they're out in the world, I should imagine it becomes perfectly plain.
My own midwife years ago had various anecdotes about pervy men and breastfeeding, simply from home visits (husbands).
Men showing up at breastfeeding support groups are not going to be able to, and in many cases won't even want to, hide their enjoyment.
I'm reminded of a woman on here who used to answer the phone for the Samaritans. Several men every, single, fucking day, would be phoning up to get off on having a woman at the end of the phone. Likewise rape crisis helplines.
The women at the Samaritans were told to keep going with the call, 'just in case.'
Some men will do literally anything to get their rocks off, and a good proportion of them don't mind who knows it.
There will be very many people at LLL who knows exactly what's happening, and some of them will be fine with it.