Who says it's irrational? It's a matter of perspective, and culture is alI about perspective. Is preserving and protecting one's culture irrational? Is allowing a dominant minority of immigrants to refuse to adapt to the culture rational?
How many free, pluralistic and democratic countries such as France or the US mandate standards of clothing other than minimal required coverage?
How is choosing a more modest swimsuit style for ONESELF - refusing to adapt to a culture that has, up to now, imposed no standard on beachwear other than minimal coverage?
If the dominant culture prefered wearing thongs and you were highly uncomfortable wearing them - should you be forced to? Maybe in Saudi Arabia where there are no individual rights (subsitute Burka) - but in a country like the US?
This is not about clothing. As I have said, thie issue is not strictly the burkini per se. This is aobut a refusal to adapt to the culture. I have spent a lot of time in France and a have been noting the impact of the large population of Muslims there. They are mostly poor, uneducated, religious people who come to France for economic reasons. They don't embrace the culture nor do they adapt to it. They scorn French customs and perspectives. They take advantage of the freedoms (such as wearing whatever you want) and better economic conditions but do not embrace or love the country itself. That is the statement the burkini makes. The French are offended by this and quite rightly.
Then perhaps the thing to do is not to ban an article of clothing that allows these women to enjoy the beach - banning it will do nothing to encourage integration into French society and will more likely have the opposite effect, creating increased isolation and division because they won't go out.
I'll give you a parallel. In Minnesota (I think) is a significant community of Somali immigrants - refugees resettled there. Their community is in an area with many lakes and bodies of water, and drowning deaths are not uncommon. Most people know how to swim, and there are many town programs sponsoring swimming lessons. The problem is that the Somali women and girls don't know how to swim, and there had been a number of drowning deaths. Because their religion forbids them from uncovering themselves around strange men, they were not able to take part in any of these programs. The local police department together the YMCA put together an ingenious program. They set up an hour one night a week for women/girls only swimming - no men. It was open to all women and girls, in any style of swimwear, not just the Somali's. They learned how to swim, but more than that - they met new people, and made friends in the community. These people had been through a lot of trauma The girls were becoming more confident, and making new friends in school. It was a win-win for the town, for the Somali refugees and for successful integration into the community.
It wasn't all lightness and honey though - there were those who protested, who claimed it was giving in to "creeping Sharia" etc. They could have just said - screw those girls and women, if they don't want to accept our culture and swim with men and wear western style swimwear - then they can stay at home. What would that have accomplished? Better integration? Or more isolation?
It seems in France, a burkini is a means of allowing women who might otherwise not go out and mingle on a holiday beach or in the water just like any French person, a chance to do so and the more they mingle, the more they are going to learn about each other. If France has an integration problem - banning the burkini is not going to solve it.