A few points:

France doesn't have this ideal of absolute individual freedom like Americans do, in France it is expected of the state to intervene in people's privates lives for the greater good. As an American you may find this horrible but that's the price you often pay when you live under a welfare state: the state will take care of everybody but that will include putting limits on what you can or can't do/say/wear.

France has a very strong secular tradition, bullying/criticising/mocking the church has been a common past time for many intellectuals for the last 200 years. When religion becomes too visible, French people always feel uncomfortable, especially when it is a newly arrived religion with a terrible track record on social issues.

Some will see this burkini issue as a simple matter of personal freedom, others as the symptom of political Islam becoming more visible. Because Islam has become more visible in France, from demanding halal food in schools and restaurants, to having women days at the swimming pool, it is changing secular France.

My personal opinion is that we should let people wear whatever they want but I'm also really saddened that politicians have done to France, we were getting rid of Christianity but now we're facing an even worse religion.