Bitcoin mixers can be trusted in a way you trust your friends who know your secrets. It depends on your friends whether they tell your secret to someone else or not but keep in mind that friends can be tortured to reveal your secrets.

Keep in mind that Blockchain analysis and tracking methods are improving daily. You not only need to trust bitcoin mixers but to trust your computer's software/hardware, trust your OS, trust your Browser and then trust your mixer.

There are problems that you should always keep in mind:
1. Mixer will scam you and not send your coins.
2. Mixer is run by authorities.
3. Mixer stores your log and data.
 3.1 - Mixer may sell your data
 3.2 - Mixer may reveal your info/data if they get in trouble with authorities.
4. Mixer website contains viruses.

There are chances that you'll experience at least one problem from the list and there are chances that you won't experience any listed problem. This is the situation where you have to trust their words, it's a risk anyway.

I want to tell you one thing, if everything that you do is legal and you just wanna hide your legal transactions, then you can feel secure by using popular bitcoin mixers. If you do something illegal, which I hope you don't do, then trust nobody or every trust will carry serious potential risks.