I just confirmed that for the modern cards gray skin, the active tab mouseover state text color is indeed red (not pure red, but reddish).
When using that skin, if you click on a previously inactive tab the text will turn red as you click on it, and the red color remains red even after you move your mouse off of the tab. Once you click on anything else though, the text color reverts to the skins specified active tab text color (dark gray/black). I believe this is what you experienced, and why you said "sometimes it stays red, sometimes it doesn't".
This finicky text color behavior is an issue in a few places in every skin, and is one of the reasons I chose not to use unique text colors for each of the four tab states on the skin I created. I simply used two text colors... one for active & active mouseover, and one for inactive & inactive mouseover. Otherwise, it just seemed like overkill of flashing text colors as you hovered over tabs.
If you want to still use the modern cards skin gray but stop the strange red text behavior, you could modify the skin XML file yourself. You would just need to make the active tab/active tab mouseover text colors the same - both red, or both black, or both whatever color. Bottom line, if you make them the same it will stop the text color from behaving weirdly.
Note that if you do this, every time there is an MC update your edits will be replaced - all the modern cards skins are part of the default download, and thus all those skins get overwritten with each MC update. So not only do you need to copy the existing skin into a new folder, but you must also modify the first line in the XML that has a variable for the skin name. The name specified within the XML file is the name you see in the view menu skin list - NOT the folder name. It is kind of hard to explain, but if you decide to play with this, you will see what I mean.