Current stats have the Catholic population (judged by registered members - people who are on the roles at a local parish) at about 77.5 million people, which would make about 5,430,000 people who object, or about 1.8% of the full US population, or statistically insignificant.
And the numbers don't surprise me at all. Though they may take issue with the practice/reality of transsexualism - the question was about civil rights, and the Catholics in the US have always been (because of being on the short end of so much of this) pretty liberal, in that they feel that civil society should not prohibit something just because some religious group does not like it or approve of it.