Exactly. Which is the feel Abrams was going for in Trek 09 and STID. There can be disagreement on the execution, but the tone and spirit certainly carried the 60s feel.Is that how they respond? It's quite normal for propaganda groups to spread contempt for something they consider politically dangerous. Whereas the original Star Trek might deserve some of this contempt for general primitive TV cheeseballyness it was in no way any more cheesy than most of the other 60's action/adventure shows and really fit right in with them.
Regardless of what GR wanted later on, I think that Abrams did well with the TOS style adventure with some social commentary. It may not be like TMP or TNG or other later Trek works, with humanity evolved. It is simply a humanity who survived WW3 to explore the stars.
More may have come later, but it isn't dismissing Trek's achievements to commend it where it succeed it and critique it where it failed or didn't do things as well as contemporary shows of the time dealing with serious issues. There are many topics that have been cited that were dealing with social issues far better for the time than Trek. Trek didn't have the cutting edge on all social issues.
Trek succeed some places, lacking in others, and generally speaking quite entertaining. I think that's more than enough without making it a "warm light for all mankind" that is being belittled by those who disagree. I don't agree with all Trek's points, but I can certainly appreciate the storytelling.