Yes, I would. Simply because activists are picketing something does not mean that the reasons are valid. If I knew for certain that the business was being discriminatory, whether to gays or any other class of people, I would not cross that line, but activists (gay or otherwise) tend to be liars who demand that everyone accept their ways regardless of the truth. Lately homosexual activists are demanding that everyone bow to them and kiss their asses. Those who do not bow are castigated relentlessly. I am willing to accept homosexuals as human beings but not at the barrel of a gun.
I happen to believe that a business should have the right to refuse service to anyone and need not disclose their reasons for doing so. No one should have the right to force a business owner to provide services. Come into my place of business and ask for service and you will be served regardless of who you are. Come into my place of business and demand service and you will find an extremely stubborn man across the table. Force me to serve you such as by legal means and you will receive extremely poor product. Were I a baker that was forced to provide a cake for a homosexual wedding against my will, a tragedy would befall the cake as it was brought into the reception hall. It would unfortunately get dropped at the last minute.
The free market should regulate discriminatory businesses. That is how things SHOULD be! Unfortunately, things do not seem to work out that way, therefore, public accommodation laws are absolutely necessary. If they were not enacted, I suspect we would still be a backward, segregated nation. I support the RIGHT of states such as Indiana to pass religious liberty laws even though my faith tells me that my savior would never discriminate against a sinner... at least for my sake I hope he would not. Having the legal right to do something does not mean that one should do it. One should have the right to discriminate. But just because one has that right does not mean that one should discriminate.