To me, and possibly just to me, Star Trek has several defining characteristics as well as some tertiary characteristics. I feel that the defining characteristics have been deemed undesirable recently and people are focusing on the tertiary characteristics.
So I'd say the defining characteristics are as follows. And these are just off the top of my head and probably not complete.
1) A future that represents humanity becoming what we always hoped we would. The humans/federation represent that idealism, while the aliens represent the ambiguity and current issues we face. That way it still shows people confronting very relevant problems of humanity while doing so from the assumption that while we've already conquered much of this on our own, thus giving a bright future, we still have more to learn. It was never about making the future seem as bad as the present. It was about handling the present problems with the hope of the future. Take away that hope and it's just a reflection of right now, which is what every one else is already doing.
2) The final frontier, or "where no one has gone before" is more about us than about space. Space is the metaphor. I think, in my interpretation, this is exactly what Q was talking about in All Good Things. It's not about mapping star charts and nebula, it's about finding deeper and unknown aspects of our own humanity and potential.
3) Confronting, often times difficult, political, social, theological, etc dilemmas and challenging the viewer to go on that journey as well. Which is why Kirk, Spock, and Bones worked from the get go. They always had a bit of an ID, Ego, Superego element, even if they were often changing which represented what. It was the journey of examining these issues.
4) This is not what we want, but what we need. I think, but might be wrong, that it was Gene Roddenbery that said to give people what they need, not what they want. Star Trek wasn't (though it was in some more minor ways) about chasing and following social trends, but about doing what they think the people should be looking for. When you chase trends, you're just part of ever changing and ever fading zeitgeist of immediacy. When you strive for something beyond that, you tend to serve a different purpose. Star Trek used to inspire people to become officers, scientists, engineers, astronauts. Not because they wanted to give people what they want, but to give people what they didn't know they needed. How many people became astronauts because of Star Trek Into Darkness?
Then there's the tertiary stuff. The frosting on the cake that doesn't define the cake, but makes it more fun etc.
1) Space battles
2) Creative visuals
3) Good guys beating the bad guys
4) Excitement and thrills
I feel people have shifted the focus to the tertiary stuff, which almost all sci-fi also has. Which is what makes this, to me, Trek in name only. It has all that tertiary stuff that I can easily find a bunch of other places. Every thing about Star Trek for the last 10 years I can easily find in Star Wars, Firefly, Lost in Space (the new one) or one of the other dozens of Netflix original sci-fi shows. I feel people want crazy visuals and excitment and Star Trek is now trying to fill those needs. When people say they want Star Trek set in the distant future or to go to places where the laws of nature are all weird, it's just to get cool visuals. That's it. There's nothing to be learned or gained from that other than entertainment. And, maybe it's just me and maybe I'm way off, but to me Star Trek was more than just entertainment. Now? Since Abrams? Just entertainment.
Now, you can all dissect what I said and point out that Star Trek didn't always do all of those things and had moments that ran contrary to it, and you'd be missing my entire point. But this is why I say it's Trek in name only currently. Fun? Sure. Disco season 2 was a lot of fun. I hope the Pike show might be a bit more Trek, but I doubt it. With Pike Trek, I'm looking forward to fun sci-fi. I hope I'm wrong. Disco season 1 was just no fun at all. It was just modern typical sci-fi which I don't like much. Season 3 is off to a bad start but can always become fun the way season 2 did. Picard was just a complete mess of nonsense to me. I just don't think the people running Star Trek want to do Star Trek. They want to make a fun exciting product that the people want. But to me, that's never been what Star Trek was about.