There is often a struggle to maintain a balance between personal rights and property rights. Neither one is absolute, and both tend to be handled differently in various states.
In general, property owners have a lot of leeway regarding who is allowed onto their property. It becomes a little more clouded when it comes to property that is generally open to the public, such as private businesses. A private business can, for example, disallow people from coming on their property if they are handing out fliers for the competition and can decide their employees are not allowed to wear t-shirts to work. They can't, however, make rules restricting race, religion, age, sex, etc.
Where is gets fuzzier is when it comes to gun rights. In Ohio, any business can put up a sign prohibiting people from bringing guns into their business. They can put up a sign for the parking lot, but there is no criminal penalty for violating a parking lot prohibition, unless you are asked to leave and you refuse. But, employers can still prohibit employees from having firearms in their personal vehicles while on company property.
The main issue at hand is that not only are employees being disarmed while at work, but the employee's Constitutional right to self defense are also denied to and from work, unless they're able to find a place to park off company property. It can even force a change in plans affecting their private life. For example, a person planning on going hunting or to the range on their way home from work is unable to do so.
The flippant answer to the issue is to say if they don't like it, they can always find another job. Of course, in this economy, that's easier said than done in many cases. Plus, we're not talking about banning chewing gum. The right to self defense is guaranteed by the Ohio Constitution. So, people are forced to choose between their lives and their livelihood, a decision they shouldn't have to make.
Numerous states, such as Florida, do not allow employers to put such restrictions on an employees personal, private vehicle. Ohio should follow suit. For that reason, this is one of the reforms being sought in 2009 by Ohioans For Concealed Carry.
While workplace violence is a very real issue, treating every gun owner as a potential mass murderer makes no more sense than treating everyone who has a prescription as a drug abuser. Not to mention that a person who decides to commit workplace violence isn't going to change his mind because guns aren't allowed on the property. Last I checked, violence isn't allowed either.
Property owners should have discretion over their property, but their property rights end where your right to life begins. If they do not want to assume responsibility for and protect you on your way to and from work, they should not be permitted to take away your ability to defend yourself during those times.