It's time they ____ doing that.
WTF. "It's time they stopped doing that"? Really? So, according to that statement, it is now time that they stopped doing that? It doesn't make sense. However, "It is now time that they (will)stop doing that, does make sense.
Stopped makes perfect sense. For example "it's time I stopped smoking". If I prefix the pronoun with a preposition then it becomes "stop". For example, "it's time for me to stop smoking".