Suppose someone is trying to endanger your reputation / dignity. For example you borrowed some money from somebody and did not clear the check you drew for him for the borrowed money; he comes to your office and starts shut and make a situation in which you lose face in front of your staff. Then the following sentence which is a translation from my mother language would work in English or it sounds like something unidiomatic to you:
- Don’t play games with my dignity.
The expression "Don't play games with..." is quite common. To play games with something is to treat it without respect - to treat it lightly.
In your example, you are right "Don't play games with my dignity" would work as an expression.
However, a more common expression in English would be "Don't play games with me". That is often heard and covers all aspects of your dignity and reputation. It also implies that the person to whom you are speaking is trying to deceive you.
