Even if the government may deny permits to people based on various reasons, it may not deny permits to people based on their exercise of his First Amendment rights. It doesn’t matter if the applicant expresses speech that doesn’t share the government officials’ values, or even the values of the majority of local citizens. It doesn’t matter if the applicant’s speech is seen as “disrespect[ful]” of certain groups. The First Amendment generally protects people’s rights to express such views without worrying that the government will deny them business permits as a result.
Not supporting the speech of Chic-fil-A’s president, but this is absolutely right. The company itself has done nothing to indicate its policies are breaking the law.