1. Set it in a different town, establishing that they're a franchise of the original Ghostbusters (dropping a hint of other teams, to allow for more movies, TV shows, comics, whatever, giving more space for more stories and, from a business perspective, more money to be made).
2. Create a different threat. Could approach it as something major in a world that's gotten used to minor ghosts. Or even maybe suggest that the ghosts have "gone quiet," which leads people to think there weren't any, which invites skeptics to question the GBs, but also sets up the back story for the main threat (like maybe a major spirit is "sucking in" all the lesser spirits to power itself).
3. Avoid any kind of social or political commentary. Just don't bother.
4. Pace the humor and serious bits. Overall semi-serious tone with jokes dropped in where appropriate.
5. Let Kate McKinnon's character be a lesbian and roll with it. No big deal made of it. If she has fun being herself on screen, write it in, don't mention it unless asked, and when asked, don't run from the question. It could add some more humor (while being careful not to be insensitive, but you'd trust she would say something if it was), and would be just an extra layer to the story that's just kind of "there," without being a "big deal."
6. If any of the original cast were interested in cameos, let them provide a mentor role or moral support, or maybe have a scene where they're talking about their team's history on TV, or being interviewed about the lack of ghosts and "Are GBs really necessary?"
7. Don't give in to the temptation to make jokes based on McCarthy's body or Jones' skin color. Too easy, and also insensitive (if not to them personally, then to other people who might be bothered by it).
8. Let the supporting cast be multidimensional.
Thinking about it, it could work so well, and could have been something at least pretty decent, and not had to worry about being compared to the original too much, because it wouldn't be an attempt to replace, but rather carrying on the legacy into the future.