On the Customer 360, regarding tags section of the summary, if pickist value(s) on the picklist "Tags" field in Customer Info is set inactive, it auto hides them from the C360 Tags and also hides the options under the selection menu.
In Customers Tab, if Tags is added as a column, same affect isn't present like the C360, here all tags, including inactive show. The adding new tags from this view is the same as C360 however.
Feature request here is to hide the inacitve tags in the table element highlightd above like C360.