automation is preferred option, since OP is looking for context based actions . Many apps are available. I prefer using MacroDroid, since it is free (upto 5 macros) and easy to learn (app guides you through the settings - make sure from the app settings you activate ignore battery optimisations if using Marshmallow)
OP has confirmed in his answer that Macrodroid approach as suggested by me in comments worked and his answer covers another automation app as well
You would need two macros for this to start with ( needs root)
First macro would look like this (Triggers / Actions / Constraints are added by +)
Macro 1 : Remove notification (name of macro )
Trigger : Notification → Notification Received → Select Application → Choose App → Text Content → Contains (Notification Text which you wish to disable)
Actions:
Configure App Notifications → Choose App →Disable
Constraints: No Constraints
Logic: We need to identify the content of notification to disable this notification from appearing. Not specifying any Constraints means we want the macro to always run
In the next macro, we make sure that if the content of notification is anything else, that notification is shown
Macro 2 : Enable notification (name of macro )
Trigger : Notification → Notification Received → Select Application → Choose App → Text Content → Excludes (Notification Text which was disabled in earlier macro)
Actions:
Configure App Notifications → Choose App →Enable
Note:
Tested and working on Moto X Play, Android 6.0.1, with a different app, since app in OP doesn't work in country
In my experience, heavily modded OS's like Samsung, Huawei, MIUI at times produce unexpected results, so it is better to have two separate macros - easier to troubleshoot from the app logs.
Optimal approach
Once you have them working satisfactorily, you can elegantly combine above macros to have a single macro (not tested by me since I don't have any apps that produce multiple sticky notifications but should work). This is a better approach, since notifications aren't lost as pointed out by OP in his solution
This will dismiss any other notifications that also happen to open from the same app at the same time.
Macro : Enable / Disable notification selectively
Trigger : Notification → Notification Received → Select Application → Choose App → Text Content → Any
Actions:
If Clause → Add Condition →Notification Present → Select Application* → Choose App → Text Content → Matches ( Notification Text for which you wish to disable )