Let's play a game of pretend. Let's say there's a huge, multinational fast food restaurant named Beef-pat-T. Now, Beef-pat-T is a family-owned business and these owners are Christians. They're so Christian in fact that Beef-pat-T stores the world over are not open on Sundays so that their employees can enjoy a day of spiritual rest and worship.
If you are a Christian, you probably think that's awesome. If you aren't a Christian, you probably think it's a little weird, but, hey, it's none of your business.
Now, at some point in time, you see an interview with the current big kahuna of Beef-pat-T that one of their guiding principles is that Christians should be free to worship.
Sounds pretty noble, doesn't it? Unless you're a raving, foaming-at-the-mouth anti-Christian, you're probably pretty okay with plopping your $10 bill down on the counter in exchange for some delicious Beef-pat-T fare.
Then you find out that Beef-pat-T has a charitable giving arm that donates to Christian groups that defend Christian religious freedom. Still awesome, right? Even if you're not a Christian, you're probably pretty down with them having the same freedoms you enjoy.
Then you see somewhere where in an interview with a Christian magazine, the big kahuna said he believed non-Christians are going to hell and are less moral than Christians. Now, that's a little discomfiting if you're not a Christian, but lots of Christians believe that. For most folks, the beliefs of the company head aren't relevant to whether they're going to buy his product, though some folks might decide to take their business elsewhere.
You then learn that this corporation doesn't mention religious belief in their non-discrimination policy. Sure, in the US, an employer can't fire someone for religious beliefs, but that doesn't apply worldwide. Are you more iffy about giving this group your cash?
But what if you found out some of these groups they support are associated with hate groups? Well, you might be curious what that means. Is it just because they share the belief that non-Christians are going to hell? So you go and look up why these are hate groups and you find out that some of these groups claim there's a non-Christian agenda to destroy Christianity in America. They claim that Hitler was a Wiccan and the worst Nazis were all pagans who created the Holocaust. They claim that Jews and Moslems are pedophiles who have an agenda to get their religions accepted in America so that they can target your children. They're actively campaigning to support employers' rights to fire non-Christians, to allow bullying of non-Christians by Christians due to the bullying being due to Christian religious belief. They use flawed and long-dismissed research or misrepresent good research to "prove" that non-Christians are bad parents who should not have custody of their children. Some of the groups have even actively campaigned in other nations to have various non-Christian religions criminalized so that non-Christians would be rounded up, imprisoned, even executed. These groups, you learn, are not considered hate groups because they hold that non-Christians are going to hell, but because they actively defame non-Christians. They aren't so much supporting Christian religious rights as they are opposing non-Christian religious rights.
And Beef-pat-T gives a portion of its profits to these groups. This is what the big kahuna cheerily admitted in his interview with that Christian magazine and claimed to be just supporting Christian religious rights.
Is it really a responsible choice to give Beef-pat-T your money?
This is the situation with Chick-Fil-A, traditional marriage, and anti-LGBT hate groups. No one is trying to force Mr. Cathy to stop believing that homosexuality is condemned in scriptures. No is asking him to compromise his beliefs. No one is asking him to not give his money to groups that support and strengthen traditional marriage.
What they are asking is that he stop giving his money to hate groups that use lies and deceit to harm LGBT people, who use fear to incite hatred toward LGBT people, who use malice as a money-raising scheme.
It is your choice whether to support Chick-Fil-A, but make no mistake, this isn't about freedom of belief, traditional marriage, or whether homosexuality is immoral or not. This is about whether it's responsible to give money to a corporation who is going to turn around and give part of that money to a group lobbying vis deceit to allow children to be beaten up in school without consequences, to have men and women executed by their government, and to tear children from their parents.
This isn't a matter of Christians vs. the LGBT lobby. This is a matter of groups using a Christian image to justify anti-Christian behavior.
Watch out for false prophets. They come to you in sheep’s clothing, but inwardly they are ferocious wolves. By their fruit you will recognize them. Do people pick grapes from thornbushes, or figs from thistles? Likewise, every good tree bears good fruit, but a bad tree bears bad fruit. A good tree cannot bear bad fruit, and a bad tree cannot bear good fruit. Every tree that does not bear good fruit is cut down and thrown into the fire. Thus, by their fruit you will recognize them. -- Matthew 7:15-20
Edit: Some people will use the excuse that other companies are just as bad or worse than Chick-Fil-A. They are quite right that corporations are often quite immoral or amoral. The consumer needs to be aware of his or her impact and choose wisely. You will make mistakes and end up supporting corporations that do not follow your values all the time. This doesn't excuse someone from knowingly supporting a corporation that is funding hate groups. And it certainly doesn't excuse people who are claiming those who are choosing not to eat at Chick-Fil-A are being anti-Christian or opposed to Mr. Cathy's freedom of speech and religion.