They can't so let's say they banned all activities relating to Bitcoin like trading, mining etc globally, the forum would still exist and even become more stronger because now the whole 'when moon' topics and price discussion will be taken out of the pictures and more focused on building a community around Bitcoin will come into effect.
Now let assume there was to be a targeted attack on the forum with the hopes of the government thinking, if they successfully bring down the forum then the trust in Bitcoin will decline, I don't think they can do anything possible to bring it down too as all their attempts will be countered.
If all the government simultaneously banned the forum in their respective countries and the server which it's hosted on gets taken down, I'm pretty sure some other solutions will be deployed immediately. like the forum been hosted on decentralized server or probably the forum goes all dark web mode lol. One thing is certain, the forum is here for good and can't think of any possibility of it going out of existence unless it was caused by the internet going down.