I'll start by saying I watch and enjoy other shows which explore LGBT issues, like Orange Is The New Black and Transparent. That being said, I do think the adjectives "preachy" and "heavy-handed" could be used to describe some of the scenes of what I've seen so far, but it's not because they deal with LGBT issues.

For one, there are many times when they violate the rule of "show don't tell" for good drama. So Nomi talking into her webcam about why she's marching is definitely showing and not telling, as is Kala doing a full soliloquy in the temple about why she doesn't want to get married. Also, I'd argue there's very little inherent drama to Nomi marching in the pride parade in San Francisco, the most LGBT friendly city in all of the United States. There's no drama in that scene because no one is opposed to it-- there is no antagonist working against her goals. The only hint of drama in the whole sequence is the mother opposing Nomi's transition. I'm certain there parents who have issues with having a transgendered child, and I'm certain they don't respond well even in a dire hospital situation, but I think the drama ends up feeling heavy handed when the mother is comically evil, rather than trying to make her a well rounded character in her own right. I'd put the White Savior Cop in that same category - really, he's the only cop in all of the South Side of Chicago who is willing to save a shot black kid? And an ER nurse would give a cop guff about carrying a shot kid into their ER? That seems unlikely, and like he's being as a wooden prop to make a point about an unjust society rather than tell a good dramatic story which also highlights aspects of an unjust society. I do think you can make these same points, but when the characters feel like obvious props to make the points, it ends up feeling preachy. I mean, I'd argue Breaking Bad was a great drama which also highlighted healthcare inaccessibility-- supposedly audiences in the UK initially didn't understand why someone with cancer would be driven to a life of crime because they have the NHS.