(Long reply, sorry)
I think that unfortunately the timing is way too late for Catholics
per se, as an organization, to make a significant dent in popular assumptions. I’ll have to frame it within other issues to explain myself:
When the idea first arose so many decades ago, of “test-tube babies,” the Catholic Church did the right thing. They stepped up to the plate and voiced the appropriate level of alarm, without hesitation and with no equivocation. Unfortunately after that they dropped the ball on the whole spectrum of designer reproductive technology until the issue of cloning came along. Between the first test-tube baby and the first animal-cloning discussion and incident, the Church virtually disappeared from the public forum. In those intervening years sperm banks by the hundreds came into existence, deliberate single motherhood came into casual acceptance (now it’s called “Choice Moms,” which does
not refer to supporting an accidental pregnancy through full term), and exotic lifestyles in general multiplied, becoming a casual fact of modern life.
It’s difficult to regain a credible voice when for so long you’ve been silent on forms of parenthood other than live man + live woman in committed exclusive relationship, and how central and fundamental that is to the fabric of society. Naturally it’s always been in the teachings, but the NYT does not sit down nightly and read The Catechism, or the Encyclicals. For decades there has been no consistent, credible, public Catholic voice on the essential unit of rearing children. In the public’s perception, the Catholic Church cares most about:
(1) abortion
per se
(2) homosexual activity
per se (and “the lifestyle”)
The Church does have a public voice about some other issues such as euthanasia and embryonic stem cell research, but those of course do not address the OP’s question, which he named “homosexual rights.” There is of course a civil right to be a practicing homosexual, as the government does not try to control sexual activity. There is a universal right for all individuals in the U.S. to share the same explicit constitutional rights, as well as implicit ones that the courts themselves have interpreted/defined as embedded in the Constitution. (That includes free private and public association with other adults, barring any authorized restriction such as age, injunctions due to criminal acts, etc.)
Only recently has the Church become more public about its opposition to gay “marriage.” Meanwhile there’s been a lot of water over that dam. Very difficult to reverse the course of those floodgates at this point, despite some of us having carried this important issue permanently affecting the
Life of children for very long now, without much assistance.
Catholics yes, should continue to oppose same-sex “marriage,” but they’d better be ready to answer why for so long they were so silent on the formal single-sex raising of children with absent fathers who were merely anonymous sperm donors, and why they’re still pretty much silent about this. Because both lifestyles objectively present the same thing: they create households in which the essential biological man+woman unit are missing. Straight women may have lots of male friends, but those aren’t fathers to the children, unless one of those men comes along, does love the woman, does adopt the child, and this adoptive father becomes a permanent part of the household, creating a traditional family unit. Merely “having opposite gender influences” does not suffice for a child. It affects a person’s security and identity to be able to relate to two primary adults of different genders. It’s more difficult in situations of separation and divorce, but at least there’s a conscious identity there that can develop over time, if both parents work at that, preferring the ultimate good of the child to the dynamic of their personal differences.
Single parenthood by accident is not the same issue as single parenthood by choice and design. But the church has also not weighed in much publicly on this general issue as well. We can say all we want to about how internally we understand what the Church says, but the outside world sees a preoccupation on the church’s part with externals, technicalities, end results, and with actions on the periphery, vs. situations, causes, and principles which are central to those issues but not being discussed much
in the secular arena.
Answering OP’s question, I say, continue to go the distance, but be ready to articulate to your opposition why the Church is steadfast against SS"M" but lukewarm about single Moms with their “designer” babies and invisible, apparently disposable, sperm-donor Dads.
And you’d better be able to use non-Catholic language. The secular public doesn’t get “ordered” and “disordered” and is not terribly fond of the term “natural law.” (Some understand it; some don’t; some misinterpret it.) The Good of Society they can relate to. Wholeness and health are terms they can relate to. Future generations, psychological integration, emotional balance, marital role-modeling between the genders – all these they can relate to. If you’re going to register contempt for these terms as being too secular for your taste, then you (the Church, its members) will continue to lose battles in this arena: in public perception, in voting booths, in the courts. And a huge amount of the latter two are affected by the first.