While your state does not have any specific statutory provisions that would protect an employee who engages in lawful off-duty conduct, I would recommend caution in using such information as the basis for discipline or other harmful employment actions such as restricting their ability to work.
Certain elements of employees’ off-duty conduct (such as attending church for example) may be tied to protected characteristics that could make such actions discriminatory.
Additionally, if engaging in such activities is permissible under state public health ordinances then it may be inconsistent to object to their off-duty conduct as being a threat to workplace safety. If there are not activities prohibited by the state law/executive order that you could point to then you could point to the general CDC guidance recommending that individuals socially distance themselves and avoid gathering in large groups
You would also want to provide some type of advance notice to employees that make it clear that their engaging in certain off duty activities could result in their access to the workplace being limited. You would want to distribute the CDC guidance (found here) to make employees aware that if you find evidence that they are not following such guidance in or out of work that they may be asked to remain outside of the workplace for a specified period of time in the interest of providing a safe work environment under OSHA’s general duty clause.
However, taking action on off-duty behavior can be complicated unless an employee is self-reporting it as your awareness of it would otherwise be coming from third party reports which may not be reliable. You would generally want to have some other type of evidence other than a report by others before taking harmful employment action against an employee.
Again, it may be fine to communicate your expectations and to ask employees about whether they are complying with social distancing recommendations outside of work. Such inquiries may not be viewed as invading an employee’s privacy too much, where it’s a public health recommendation. It may be more complicated to take action if an employee admits to violating CDC guidance or trying to prove it if the employee denies it.
If you have ongoing concerns about workplace safety, then you may first consider using screening procedures (asking employees if they are experiencing symptoms or even temperature checks) and perhaps require employees to wear cloth face coverings as an alternative to potentially disciplining for off-duty conduct.