I think it's a matter of face. If word got out that a company had a crossdressing man as a manager, then the company would lose face. Although, personally, I'd be really happy to have a crossdressing manager if I owned a company cuz why not
Because most Japanese people are extremely reluctant to accept new things/concepts (in this particular story -> crossdressing, trans, gays). It's part of their culture. So when everyone at the company find out about his secret, it will most certainty cause a huge disruption to his work life. Stuffs like having his co-workers give him weird looks and treat him different, talk behind his back,... Eventually, those rumors will reach the ears of higher-leaders, and believe or not, he can be fired with reasons like: not suitable for the position anymore due to personal life scandal, which can affect the company's image, workplace environment, etc.
Why is it that his second job would get him a dismissal... It doesn't effect his other job in anyway. I knew plenty of ladies and men who worked as strippers as a second job.
This confused me.