I'm surprised that you can be against behavior control by some types of economic coercion (taxes) yet support other types (employment).....
You're killin' me dude. You don't see a difference between government taking your money through taxes, and employers declining to give you their money through employment? You don't see how government forcing an employer to work with people they don't like is the actual coercion that is going on in this country? Are you seriously saying that, if I don't hire you, I'm forcing you to do something?
Obligated?.....No. But, if a parking lot owner allows me to park on that property, it does not mean the lot owner has permission to violate my civil rights to search and property. Whatever is in the car is outside the reach of the lot owner. If the lot owner doesn't like it, he should reconsider having the parking lot open to the public. If the lot owner suspects criminal activity, that's what the police are for.
Who is violating your civil rights by searching your car? If that is about to happen, you should have the option to leave. If you are not allowed to leave, then you can start talking about your civil rights. Since you have no right to be in someone else's property, you can't claim a right to do anything on that property, or take anything into that property. Your presence there is solely at the discretion of the property owner. The one thing they have to let you do is leave. And that's it.
Furthermore, there's no reason why "open to the public" should entail a surrender of property rights. As a property owner, you should have the right to invite the general public into your property, but still set limits on what that means. If you're selling your house, you should be able to have an open house, without letting people using your bathroom or sleep in your bed, or watch your TV. There's no reason why you shouldn't be able to decide who will be allowed in, and how they will treat your property.
Why do you want the civil rights of property owners and employers to be violated?