There are lots of places to defend violated civil liberties. This isn't one of them.
So they've charged them with various crimes, and a jury may or may not convict them. But the trial hasn't happened yet - what right does the government have to take down their website and business just in case they get a conviction?
Every right. They shall not be deprived of life, liberty, or property without due process of law. But "due process" is just "the process that is due under the circumstances." If I see you shooting your wife, I can lock you up even though you haven't been tried yet. That doesn't mean I have to let you out to shoot your neighbor until you get a trial.
Isn't the whole point of "innocent until proven guilty" that you get your day in court before any punishment happens?
No. "Innocent until proven guilty" is also a presumption, not a fact--courts don't find people innocent, they find people "not guilty," which does NOT mean they're innocent. It just means that either the state failed to make their case or the jury wasn't listening. Juries don't always pay attention. Occasionally a person is actually innocent. The system is very bad about helping people who are actually innocent.
The point of innocent until proven guilty is basically the intuitive belief that it is better to have ten guilty men go free than to send one innocent man to prison. Effectively, we have a very strong belief that people should never be sent to prison unless they are actually guilty. (We are either "retributivists" or "side-constrained consequentialists," but the side-constraint of "must actually be guilty" is there for pretty much everyone.) But it's not an absolute prohibition on denials of life, liberty, or property, because you can't just let people go around murdering or stealing or money laundering while you're waiting for the trial.
Most or all of the people in this story are guilty, with an extremely high degree of probability. In the process of getting rich off of a massive criminal conspiracy, they got kids raped. They're lucky they're not put up against a wall and shot.