An interviewer can't see anything about your history except what you tell them, and any decent interviewer will know not to take your word as gospel. So you need to look at anything you say through the eyes of a person who knows is making a guess at the accuracy of everything you say. It's totally possible that if you say your old employer has a culture of distrust and hate, you're telling the absolute truth. It's also possible though that you are a problematic employee and you're bitter because you were fired/pushed out for being unpleasant and incompetent. So you need to be careful how you present your story so that it's hard to interpret negatively.
I've seen employees who really didn't do anything useful. I've seen managers work with them for months trying to resolve issues. I've seen those same managers resort to micromanaging because at some point that's all you can do. And I've seen those problematic employees finally get pushed out and then rant on Facebook and in person about how terrible their manager and/or the company were, when I know for a fact that they were the bulk of the problem.
Imagine if you asked the interviewer how they felt about their current employer and they told you it's pretty good except that the guy you're replacing was terrible, that he was incompetent and constantly angry and despite constant oversight he never delivered anything of value. This should be a point of concern for you. Was the previous employee the entire problem? Is the position overworked? Did manager deal with it but berating the employee to just do more rather than working with the employee to fix the problems? And will the company badmouth you to others if/when you leave?
A bad employee stays a bad employee, even though he hides the truth by not bitching and a bad company stays bad, even though nobody dares to talk about it. But with honesty people find out those things more quickly ...
If you want to speak up at your current employer to resolve issues, I would generally encourage that. There's clear value in being honest with your employer and trying to work out issues (though there can also be risk if you have a really unhealthy relationship with management). Being "honest" with an interviewer about your current company doesn't solve anything. You won't fix problems with your current employer by telling a new company about them. You won't likely discover anything useful about the new company. And they won't likely learn anything useful about you, because it's impossible for them to tell if you're just bitter and spiteful or if you had legitimate problems caused by the company.
If the legitimate reason would be, that they micromanaged everything, because of lack of trust, even though I delivered results and that the general atmosphere were a mixture of hate and distrust, then I would very much say so in the next interview, if asked. And if they then won't take me, I would assume it is because the new place is similar and they just don't like people talk about it. So no place where I want to be anyway ...