I am planning a SharePoint 2013 on-prem patching, current SharePoint build number is 15.0.4569.1000. I also have Nintex installed current version 188.8.131.52. If I patch SharePoint with current patches do I have to also patch Nintex? If I don't, will Nintex break?
afaik the SharePoint build number has no correlation with the Nintex Version number at all, you cannot download Nintex for a specific build number. That means you should be able to patch your SharePoint without having to update Nintex.
However, I've never done this.