Bug#1: Install CMake Tools with a non-CMake project and the Select a Kit dropdown appears.
Bug#2: Put a breakpoint in the activation() method of another extension (e.g. the C/C++ extension) or otherwse cause "too slow" activation, which causes VS Code's "workspace contains */CMakeLists.txt" activation to switch to "" activation, causing "Select a Kit" to appear for non-CMake projects.
The fix for both of these would be to be to check on activation if the real activation conditions really occurred or not, similar to what the C/C++ extension does. Other fixes might be possible too.
Bug#3: When the above bugs are hit, then the select a kits also appears after adding a new workspace folder for a non-CMake folder.
Can we also get rid of CMake extension related UI widgets/elements like these:

If there is no "CMakeLists.txt" in the folder?
This occurs very frequently in cold start scenarios, such as when a TypeScript/non-CMake folder is opened for the first time. Also seems to occur more often when extensions are updated.
CMake Tools 1.7.0 was released today and it contains a fix for this issue. Upgrade the extension in VSCode and let us know if you encounter any other problems.
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Can we also get rid of CMake extension related UI widgets/elements like these:

If there is no "CMakeLists.txt" in the folder?