When motorcycle helmets became compulory, very few people stopped riding for that reason.
When the wearing of seatbelts by front-seat occupants in cars became mandatory, very few people stopped driving for that reason.
Similarly, when it became compulsory to wear them in the rear very few people stopped accepting lifts...
I recall heated debates in the 80s where drivers would insist that seat belts were dangerous because they would make it difficult to exit a car submerged upside-down in a lake. In all my years on this planet I've known only one person who died in an inverted car in a river and that was more due to alcohol and size than the seatbelt.
I don't believe for a moment that cycle helmets will become compulsory, but if they do then very few people will stop cycling.
I see far more cycle helmets than I did in the 60s, 70s, 80s and 90s.....
More and more new cyclists will just assume that helmets are desirable and will buy them.
I don't imagine there will ever be any need to make them compulsory.
I often go without a helmet, but I'm in a minority on that.
I think if it came down to a national debate (even a referendum!) the vast majority of people would decide they had bigger fish to fry.
It's not unlike the fox-hunting debate. The extremeties on either side have little else that makes them crosser, but most people find other things to occupy their minds.
So... If helmets bcome compulsory, not much will change.