I believe the owner of Chick-fil-A has the right to spend his own money to promote his own views, however much I disagree with them. Here are some quotations that support my position:

George Washington:

If men are to be precluded from offering their sentiments on a matter which may involve the most serious and alarming consequences that can invite the consideration of mankind, reason is of no use; the freedom of speech may be taken away, and dumb and silent we may be led, like sheep to the slaughter.

Thomas Jefferson:

I never … believed there was one code of morality for a public and another for a private man.

 

I tolerate with utmost latitude the right of others to differ with me in opinion without imputing to them criminality. I know too well all the weaknesses and uncertainty of human reason to wonder at its different results.

 

I would rather be exposed to the inconveniences attending too much liberty than to those attending too small a degree of it.

Benjamin Franklin:

Without Freedom of Thought there can be no such Thing as Wisdom; and no such Thing as Public Liberty, without Freedom of Speech.

 

In those wretched countries where a man cannot call his tongue his own, he can scarce call anything his own. Whoever would overthrow the liberty of a nation must begin by subduing the freeness of speech.

Edward Beecher:

We are more especially called upon to maintain the principles of free discussion in case of unpopular sentiments or persons, as in no other case will any effort to maintain them be needed.

I also believe that those who disagree have the right to express their opinions, up to and including boycotting Chick-fil-A. That, too, is freedom of speech.