You can use any valid css selector it doesn’t have to be an ID. The component in the background uses the document.querySelectorAll method for finding the appropriate node.
Besides the sting selector you can also pass a HTMLElements as the first argument. This might help you in case of shadowDOM elemets which are not part of the DOM.
Here is an example:
const dateInput = el.shadowRoot.querySelector('.bday'); // accessing the shadowDOM elements throught the shadowRoot interface
const dateInst = mobiscroll.date(dateInput);