Accepting that a property owner has a legal right to do something is not the same as supporting ownership rights. Criticizing a decision by citing reasons why it would be ineffective or even detrimental to its goal is one thing, but the posts I referenced aren't doing that.
What they are doing instead is expressing disdain over the exercise of ownership rights to do something that the critic finds personally offensive in an ideological sense. In other words, they profess to support ownership rights only as long as that owner does what they want.
Maybe this one question quiz will help in thinking about the issue a little:
1. Bob paints his house pink. Which of the following people could be considered anti-property rights?
a. Cindy tells bob she hates it
b. Matt stops inviting bob to his parties, and tells everyone how stupid Bob is for painting his house and ugly color.
c. Steve goes to city hall to file a complaint.
d. Eric paints his house green in retaliation because he knows Bob hates green.
e. all of the above
(answer c)
I disagree. It appears that what you have problems with is the Constitutional right to free speech. You have a legal right to buy the house next door to me and paint it orange with purple polka dots. I would then have the right criticize you and your paint choices without being opposed to property rights.
Here, Ford has a right to restrict parking in their lot, and I have a right to point out how stupid it is as a business decision, and to translate that disdain into a purchasing decision.