Hello Emma,
In my personal opinion, both are incorrect though even native English speakers would say the same thing. I think what you really mean to say is;
"They are using their belief as a reason to be criminal and violent."
Or perhaps;
"They are using their belief as a crutch for criminal and violent behaviour."
However, if you want to use mean in the sentence, you would say;
"They are using their belief as a means to be criminal and violent."