I tend to the latter and then let the free market decide if they want to support a business that is willing to promote the KKK or a gay wedding or NAMBLA or whatever event it is.
When I was stationed at an airbase in upstate New York, there was a Christian bookstore that had bought a big commercial building and was in the process of re-furbishing it to expand the room they needed as their business grew.
One of the things the building had was a bowling alley in the basement area, with a separate entrance in the back. Rather than gutting the bowling alley, they decided to re-furbish that, too, and re-open it as a family friendly venue. Critics laughed and said it would go broke within ninety days, because there was "no way" a bowling alley could stay in business without offering the sale of alcohol, tobacco, and loud, secular music playing in the background.
Much to their shock, it became one of the most successful alleys in the entire city; turns out that families
liked having an alley they could take their kids to and not have them exposed to alcohol, tobacco, and nasty secular music, just a good, family-friendly, fun time. Church leagues started nearly immediately, as well as various Christian clubs, and very soon, the bowling alley was pulling in nearly more money than the bookstore was. It reached the point where the other alleys were losing business, because the church leagues, etc., switched to the Christian alley.
I'd say that's a pretty fair example of the free market and personal choice made the decision as to whether a venue survived or not.