I have a slightly different point of view on Fenders. First of all, I really love them, but maybe not for the reason many people do. Sure, they have a clearly recognizable sound, and although people would love to own instruments that are made by craftsmen rather that factory workers; there are times where mass produced may be exactly what you want.
Fenders do vary, and the American Professional line that is out now does in fact sound, play, and feel differently than the previous iteration, which was the American Standard. I'm also a jazz bass lover, and can't say enough how great this style of instrument is! That being said, I've played a lot of j style instruments out there. I've played Sadowsky, Lakland, Mike Lull, Penza, G&L, and various other instruments.
I will say that Mike Lull and Penza may have been at the top of the non Fender J style instruments for my tastes, and the build quality of Sadowsky is incredible, but I wasn't the biggest fan of the sound. Just like Fender, many boutique style basses aren't all the same either. Many of the most beautiful basses that I tried that I was sure I would like just didn't have the "it" factor that I wanted(some did too, but there was no way I could buy them).
What I've learned is that many of these instruments, although they're J styled instruments, don't sound like a Fender. Many of them don't truly feel like Fenders either, and I mean that in the best way with no disrespect to builders. My favorite Fender is a Custom Shop Custom Classic 4. I tried it originally in 2004. I just finished high school, and there was no way I could get it. Finally last year I got one that I was able to find used. It had that "it" factor for sure! But, I still modified it... It now has a new bridge, new preamp, new pickups, soon to be a new pickguard, and I'll probably refinish it from Fiesta Red to Gunmetal Flake.
I love Fender because if you find that bass that just has it where you need it in all the right places (not just the same model, but a specific bass sometimes), then you should go for it! Fenders have the ability to grow with you, and their sound can change as your needs do too! What you can't really change (without it being easily reversible), is the way a body resonates, the feel of the neck, or the fit and finish. If you find something that just feels special, and really checks off most of the boxes you have on the top priorities you want in a bass, then you should go for it! It is a solid investment of your money, the time you'll spend playing the instrument, and hopefully a relationship you build with music as you continue to play throughout the years.