But where do you personally draw the analytical line?
That's a good question, deserving of a good, simple answer (with explanations). Basically, whatever things were meant to be taken seriously, should be. And whatever was not, should not. I'll use your examples:
1. The Wolf 359 ships: These should be taken seriously. The TNG producers contracted out a professional modelmaker (Ed Miarecki) to design and build six new starship classes. They could have easily just thrown together a bunch of model kits themselves, but they didn't. Okuda even went so far as to assign names, registry numbers, and class designations for these ships, and added their info in the Encyclopedia. The resulting designs (and the two ships Greg Jein built) are 100% realistic.
2. The Frankenstein fleet: These should NOT be taken seriously. In complete opposition to the Wolf 359 ships, these models were simply rushed bash jobs that in many cases make no logical sense the way they were built. They were not made by professionals, they were not given class designations, and the ones that did have names and numbers were given them by whoever slapped them together, not someone official like Okuda or Sternbach. Yes, some of them were seen on screen, but YMMV as to how much one should actually take them seriously.
3. USS Kelvin NCC-0514: Name is Abrams's granddad, and number is allegedly his birth date. This is an homage, not an in-joke, and because the number fits the time period, there's no problem. The Kelvin kitbashes were the same deal.
4. USS Bozeman NCC-1941: The registry is not a joke; again, it's an homage to something. Because the number happens to fit the age of the ship, like the Kelvin there's no problem with taking it seriously.
5. Elmer Fudd, NCC-42 et. al from Conspiracy: No one at the time would have ever guessed that this info would ever be readable, or that Trek fans would obsess over this info to the extent we do here. A lot of the info was just random jokes, and was thrown together very quickly, spelling errors and all. Nothing in it should be taken seriously. As I said before, once we get all the info, it's going in my shiplist for completeness' sake, but other than that, it's meaningless to me because it was meaningless to the people who made it up.