I have been testing out the datepicker for a project I am working on, but have found the user experience on mobile not to be very good.

I took a look at how airbnb's react-dates handle mobile and found they use a portal/overlay.

I suggest making a similar overlay for react-datepicker.
I have created PR #696 the adds the the prop withPortal which creates the calendar in a portal/overlay.
Here it is running on my project.

Happy to hear any feedback.
Pushed 0.40.0 with this included.
withPortal works great on desktop browser.
When I test on mobile, it doesn't prevent outside touch events and if I click button behind overlay, it's click event works.
And browser console says Unable to preventDefault inside passive event listener invocation.
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withPortalworks great on desktop browser.When I test on mobile, it doesn't prevent outside touch events and if I click button behind overlay, it's click event works.
And browser console says
Unable to preventDefault inside passive event listener invocation.