I used to use them in both X11 and CSS way back in the day. They were really common in X11, because a lot of users were on pseudocolor displays and it made sense to reuse colors as much as possible.
If you used uncommon colors in your program on - for example - a Sparcstation 20, the palette would shift every time you moved the mouse in or out of your window. It's difficult to describe to someone that's never seen it, but it's unpleasant. No one mourns the death of pseudocolor.
Pseudocolor was a different thing. The palette wasn't fixed. The adapter could display any color in a 24-bit color space, but only 256 colors at once. So if you had one program that used one palette and another program that used a different palette on the screen at the same time, whichever program wasn't active would have its colors scrambled.
If you used uncommon colors in your program on - for example - a Sparcstation 20, the palette would shift every time you moved the mouse in or out of your window. It's difficult to describe to someone that's never seen it, but it's unpleasant. No one mourns the death of pseudocolor.