I just found out my boss was in prison for four years for theft of over $20,000 and under $100,000. It really bothers me and I no longer respect her at all and when she gives me guidance or instructions all I see is her mug shot. Someone told me about it and I didn't believe them so I looked it up and it's true. I am wondering if it is legal to hire a convicted felon for a municipality in the state of Texas?

Yes, they can't be police officers and a few other positions.