I think we need to look at this a little more closely. Consider what is being taken here: we have a sheriff's deputy, thus someone whose very presence in a situation reflects the state's moral authority to arbitrate in dispute, who wilfully refuses to marry but would rather live like a child with a boy she then has pleasures with.
Clearly, this woman is intentionally immature and selfish, thinking maily of her own pleasure no matter the cost or disgrace. That's casting disrepute on the state (which hardly needs help in generating disrepubility [sic, likely]). It should be a matter of employment policy whether she can keep her job when she openly defies a policy she apparently knew about when she hired on. That's insubordination.
Need I go on?
Interesting point. Lots of case law in the area of how far a public employer can set standards of conduct. Clearly, most governmental offices have standards which permit discipline up to termination if an employee acts in such a way as to bring discredit on the office. Generally it has to link directly to the job and employee. 50 years ago, living outside of marriage, or pregnancy outside of marriage might qualify. I doubt if many people today would give it a second thought.
Then there's the issue of whether the "standard" is necessary for the successful execution of duties. Pretty doubtful that a moral issue like that has any bearing on her job. For example, you couldn't fire someone for getting pregnant, married or not.
Finally, there might be an out for the sheriff, if she violated a contractual agreement, but again, a judge might find it was not material to her execution of duties, and likely would be unenforceable.