Cardinal Dolan remarked that the Church was outmarketed on the so-called "gay marriage" issue and caricatured as being "anti-gay." While I agree, I think it is more accurate to say the opponents of the Church used massive propaganda and slander/libel in their marketing of homosexuality and abortion.
This propaganda and slander involves portraying their own position as true without proving it so, and then vilifying anyone who disagrees making them appear to be motivated by bigotry.
It has been quite successful. Looking at comments in news stories about the ACLU suing the Catholic bishops on their abortion directive, I see hateful comments about how the Church is a horrific institution that needs to be destroyed.
Now one needs to take Internet comments with a grain of salt. How representative they are of the population is hard to judge. Are they the common view? Or are they snarky teens mad that mom and dad made them go to Church?
However, such comments show that among part of the population people have been effectively propagandized to support, or at least not care, if the Government should try to attack or control the Church.
Basically the propagandists state (without proof) that the Catholic position is based on hatred and seek to use the appeal to emotion in order to get pity for the favored view and opposition to the Church teaching... before the Church can even speak.
Now some have blamed the bishops, saying that if they were doing their jobs we wouldn't be in this position. I don't believe that. The reason is, a false statement (whether deliberate or not) can easily fit on a slogan or soundbite. The refutation takes much longer. Given how short a news story is, the refutation is usually ignored or distorted.
However, all Catholics (not just the bishops and priests) are called to defend the faith. Not all who have been propagandized are extreme. Some of them may be open to the truth, merely believing what they have been told about us because it never occurred to question the reliability of the reports.
Some, especially on the Internet, may be abusive. All we can do is to be polite and speak to the reader, not get sucked into a flame war with an abusive person.