Continuous axes assume that there is a full domain of data that you are plotting against, so there isn't a way to cut out chunks of the continuous axis.
I have attached an example workbook where I joined a list of Saturdays to my original data source. Then I created a dual axis on the Gantt chart where the second axis white-outs every weekend. I would be happy to include directions if it looks like something you want to use.
The Tableau website has an Ideas section where customers can add, comment, and vote on features they would like to see in the product. Votes are used to help prioritize new features. Our Development team also loves to see everyone's use cases in the comments, which helps them better design features that will meet the most possible needs.
I was unable to find an Idea on this already, so I recommend creating one!
Hope this helps
example exclude weekend.twbx 14.0 KB