I still can't understand that. It's exactly the same code, it should work in both views. Or are you saying you can only use the default label once and when you want to use the same shortcode in another view, I'll have to [wpml-string] for the default_label?
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I had that impression that once the default_label registered the same string using default_label should not work but based on my latest testing for which I shared the screenshot.
I created two views, Test View 1 and Test View 2 and added the same taxonomy taxonomy filter to both view having the same label but as you can see with the screenshot, I can see the default_lable string is added to String Translation for both of the view.
Please check the following screenshot:
=> hidden link
The string "Select Gym Type" is added two times one for test view 1 and another for test view 2.
So, its working as expected.
If you see in future its not working as expected, you are welcome to open a new ticket.
Ok, based on your testing, I deleted all vertical-category_default_label strings from the String Translation table, then made sure both Views use the same shortcode and then saved them. As like in your example, both Views are now registered and in both the translated default label shows up.
Issue resolved, we just needed to delete the "old" strings prior to the default label fix and register them again.