As far as I am concerned, your employer takes it too far. What I do on my own time is none of my employer's business, as it were. If I am involved in a weekend nightclub drunken brawl, and no other company, customer, or vendor personnel are involved, and no subsequent legal or social fallout interferes with my working hours, than it's absolutely inappropriate for management to acknowledge these activities.

The very concept of "bringing disrepute" is a slippery slope, and shamefully medieval.

Edit: I'll clarify. The problematic issue is the ambiguous, subjective threshold at which activities become "disreputable." Ambiguous, subjective standards like that should not be grounds for dismissal. They are too easily abused via "selective enforcement".

Of course, in many firms, employment is entirely "at will," and subject to employers' most capricious whims. This is not a good thing; the subjugation of one's employment to another's whim is an oppressive imbalance of power.