Please take a look below. Is it ok to have nested menus like the ones shown below? The main menu is Activity/Practice and Sub menu for Practice is Me/Everyone. Is this ok to do?
The screenshot you have shown implies that you two layers of filters to show data, first is Activity and Practice while other is Me and everyone. Since you are using nested tabs for displaying data, I assume that all the information you are showing is related. Because tabs are used for showing chunk data that is logically related, and it is liable for user to switch between the information very quickly. Only in such cases you should use tabs.
Check link for more usage guideline: https://www.nngroup.com/articles/tabs-used-right/
The data you are displaying is related logically, but the style you have used to display data is not right. Instead of using tabs for Me and everyone you can use, cards that will hold category name, and will expand and display data on user click. This will remove the hierarchical nesting which confuses user making it more user friendly. check image for reference.
Also the tab style you have used is quite confusing. Here user will get confuse as in which tab currently he is. That style is valid if you have at least 3 or more tabs. Because then the user will see one tab different from other two or more tabs and it will give him a clear idea where he is currently. In this case you can show the non active tab in black, white and grey as I have shown. This will indicate clearly where the user is.
Also using cards is best solution as you can add more cards in a single tab in future without complexing the UI to more deeper level.