Excel 365 online, date formatting problem.

Ian,

Cell formatting is only to define the way how your dates will be displayed. To edit/input new date you have to use your regional date formatting as it defined in your environment (your desktop or O365 regional settings).

As for displaying the date - as soon as you transfer your file to another region the dates will be displayed in default formats of this region. Doesn't matter Excel online or desktop. If only you dind't force to keep regional format in custom format of the cell (asterisk or part like [$-en-GB] of the format string, more about that for example here https://www.ablebits.com/office-addins-blog/2015/03/11/change-date-format-excel/). Please note, Excel online itself doesn't support custom formatting, but it accepts custom formatting made in desktop application.

In brief, your users have to change/enter dates in the format they have in regional settings of their site, however you may display these dates in any format you prefer.