You don't need to trust your coworkers to organize. And they will take advantage of you if you work their shift etc and often will not reciprocate. You can acknowledge that coworkers aren't your friends while understanding that organizing is good for everyone. If someone is gonna try to sabotage your attempts at organizing that's just how it is but there's no reason to trust a coworker to pay you back. Also, I'm sorry but if you're putting people at risk I don't care how friendly you act to me I'm reporting you.
In some cases, but not across the board.
In fact, if you don't trust any of your co-workers, I'd say there's a chance you are the problem. I've known people like this and my job is better without them.