Whether one filter clears another depends on how the filter actions are configured on the dashboard. If you simply selected "Use as Filter" when building the dashboard, it automatically creates a filter action for all dimensions in that sheet. You should be able to edit that action filter, and remove the date field from the filter.
If that doesn't help, then the next step to help you will require a sample packaged workbook. If you have confidential data, please mockup something using the Superstore database, or see Anonymize your Tableau Package Data for Sharing |Tableau Support Community.