Homophobia and transphobia are on the decline. The process is moving fast with respect to homophobia. Lots of barriers (serving in the military, same-sex marriage) that seemed set in stone twenty years ago have fallen in just the last several years. Though it may seem slow to individuals in their everyday lives, this is all happening in the blink of an eye in historical terms.
Transphobia is following the same trajectory but is not as far along the same curve yet. There's a lot of work remaining to be done.
Why is it taking longer for transphobia to decline? I think it's a matter of visibility. One thing the gay rights movement emphasized strongly was the need to come out and be visible. In the 1950s and 60s, it was really tough to step out of the closet and into the open. People lost jobs, security clearances, family relationships. Some went to prison. Some lost their lives. We owe a lot to the courage of those who were first to step forward.
As more and more gay and lesbian people came out, it began to seem less outlandish to the straight world. In the eyes of the straight world, the image of gay people slowly began to change from the pulp fiction villainy most people imagined and started to assume the face of people they actually knew: coworkers, friends, family members.
If you've never met anyone gay, it's easy to denounce gay people as sinners and perverts and say they deserve no rights. But if you actually know a number of gay people, it's pretty hard to believe that your nice lesbian cousin is evil and shouldn't be allowed to marry her girlfriend. As more and more gay folks came out, the momentum increased and the barriers started to fall.
As I said, transphobia is on the same curve. It's just not as far along the track. One story in the news you might look at is the current one about the bathroom bill just passed in South Dakota. When it hit the Governor's desk for signature, he scratched his head and wondered whether to sign. He said, "I've never met any transgender people."
Actually, I doubt that. I imagine even in South Dakota he probably has met trans people, but he just didn't realize it. But he was expressing the same idea I outlined above with respect to gay people. If you don't know any trans people, it's easy to imagine them as perverted or evil and conclude they need to be suppressed or outlawed.
To his credit, that Governor took the time to meet with transgender people opposing the bill. I don't know whether it will be enough to make the difference on that specific legislation, but I think you see what I'm talking about. It's easy to discriminate against nameless, faceless people you don't know. It's harder to discriminate against actual people you meet and engage with face to face.
Part of the reason that transphobia is declining more slowly than homophobia is a matter of numbers. There's a lot of us, but we're still pretty rare. There are probably 40 or 50 million people in the US that fit under some part of the LGBT umbrella. But maybe only one or two million trans people. (It's really hard to get accurate estimates.)
Adding to our lack of visibility is the fact that trans folks sometimes just "disappear." While trans folks may be very visible during the period of gender transition, many who make the transition successfully just blend in and disappear into the cis world afterwards. There are plenty of trans folks who have done exactly that. Cis people may be working in the same office as a trans person for years without having any idea.
Although both homophobia and transphobia are on the decline, they are still alive and still dangerous. Homophobia and transphobia are being actively cultivated for political advantage by right-wing ideologues seeking the support of bigoted and fearful voters. And also for religious motives by fundamentalists seeking to reshape the world according to their superstitions and prejudices.