The expected behavior for option inputToggle is to open the picker whenever the input is clicked, not focused.

It takes to add some code to make it work as you're expecting.

import React, { useEffect, useState } from 'react';
import { MDBDatepicker } from 'mdb-react-ui-kit';

export default function App() {
  const [open, setOpen] = useState(false);

  useEffect(() => {
    const handleFocus = () => {
      setOpen(true);
    };

    const input = document.querySelector('.datepicker input');
    input?.addEventListener('focus', handleFocus);

    return () => {
      input?.removeEventListener('focus', handleFocus);
    };
  }, []);

  return <MDBDatepicker open={open} inputToggle onClose={() => setOpen(false)} />;
}