For Tableau Desktop users who publish to Tableau Server:

Version compatibility does matter between Tableau Server and Tableau Desktop. It also matters when you develop content collaboratively with other Tableau publishers—you'll want to coordinate and use the same Tableau Desktop version.

When we upgrade Tableau Server to a new version, we'll send an announcement and remind Tableau Desktop users to upgrade.

For more information, see Make Workbooks Compatible Between Versions from Tableau.

Bottom line

If you publish to Tableau Server, you should maintain your Tableau Desktop licence at the same point version.

For example, if Tableau Server is version 2019.2.3 then Tableau Desktop versions 2019.2, 2019.2.1, 2019.2.2, 2019.2.3 are compatible.