For a company to deny any individual employment on the basis of their union membership, or not, is clearly an affront that on that individual's rights to be a member of, or not be a member, of a labor union
One could also say that for the government to deny an employers' right to discriminate against persons on the basis of membership in a union is clearly an affront on his right to run his business as he sees fit.
And this argument could be used against the setting of a minimum wage as well- that it is an affront on a businessman's right to run his business- and set wages- as he sees fit. (It also undermines an employee's right to negotiate wages and set them low to be more competitive, which seems silly but happens every day in the U.S. and elsewhere) But I'm not sure where the "right to run his business as he sees fit" emanates from- is it the "life, liberty, and property" clause? Several examples in the case argument thread seem to imply so, but I don't see that having the right to own property is synonymous with having the right to use that property to become an employer- I'm not saying that right doesn't exist, but it's just not inherent in the "life, liberty, and property" clause. In real life, there is no absolute right to run a business- you must get a license, granted by a government, and by getting that license you agree to certain standards of conduct- much like you agree to certain standards of conduct when you get a driver's license.
