I find this question very interesting because it ultimately tells nothing but one's preferences for what they would like to see in Star Trek. But for me, Star Trek is ultimately made Star Trek by taking place in the Star Trek universe.
Of course, there are topics and themes that Star Trek has consistently portrayed, but even they aren't exclusive criteria. Star Trek has generally showed us a positive future where humanity wasn't discriminating against each other, eradicated most diseases and lived in abundance, at least on Earth... the frontier has always been another story. Unfortunately, many people have mistaken it to mean that Star Trek portrayed a perfect post-scarcity utopia populated by perfect people, where no dysfunctions of the system ever existed. The newer installments were excluded from the body of Star Trek by many fans because they dared to portray these dysfunctions, for which they were perceived as rejecting the positive vision of Star Trek in its entirety, despite these concepts having been there all along. Tasha grew up on a failed colony plagued by drugs and gang violence after all, and several 24th century Starfleet officers were shown to be racist and prejudiced against aliens... and, of course, the very reason that the Enterprise was visiting all these Federation colonies on the frontier in the first place was that they still had lots of problems to deal with.
These were things that Star Trek did, naturally. But these still aren't what make a series Star Trek. Voyager didn't magically cease being Star Trek the moment they left the Federation and found themselves all alone in a vast region of the galaxy filled with oppressive, hostile alien empires.