"I've been told that running a passive bass into a passive DI does not push a strong enough signal to the PA to capture the true color of the bass's signal."
I disagree with this as a blanket statement. It depends on the transformer used in the DI. Jensen or Lundahl-equipped DIs are actually preferred by some guys because of their quality of tone, even though Radial does have a note about using active DIs with active basses. I'm not questioning what you are hearing, but make sure that what you are hearing is not simply a hotter signal from the active DI giving you the fuller-sound perception.
"I tend to believe this because when I compare my sound in the house when playing through an active DI compared to a passive DI, the tone is much fuller. I've used different types of active DI's (some of which I like better than others) but regardless of which one I use, I always prefer the passive bass/ active DI combo than passive/ passive."
This is fine as it is your perception, which is the most important to you. It's your ears and your tone. You are smart to trust them, even though someone else may disagree because of their own experiences
"It also seems (in my experience) like the guys who go passive / passive are the ones that either don't care enough about their sound to invest in a good DI or they can't hear the difference."
It may seem that way to you, but as a guy with 20+ years of mixing all kinds of bands on the national level, plus being the FOH guy for several rocking Black Gospel groups and several orchestras in the area, I assure you, I certainly work hard at a good tone. I am meticulous with the condition of my basses, their action set-ups, string condition, I even have a regimen to protect the callouses on my plucking hand. And my choice of the Radial JDI over the J48 is a result of comparing the two side by side. Perhaps you've seen guys with really cheap DIs that are giving you this perception. There's $40 DIs out that make a bass sound absolutely wretched, no doubt.
"This last sentence is why I'm asking the question. I wonder if I've unfairly correlated bad bass players/ sound guys with this live bass set up or if it's more common than I realize."
I'm not sure I follow where this last sentence is going. In the live sound world, I could give you 20+ reasons for a bad bass tone, starting with a player's weak playing technique to poorly set-up PA speakers and everything in between.
The only side-by-side DI comparison I've ever done is with a Radial JDI vs a Radial J48. I own the JDIs (three of them) and the church has the J48s. The basses are my AM STD Precision 5 and my 98 EB MM Stingray H5.
The JDI, to my ears, with both basses, my ears only, no one else listening, sounded a little warmer to me, listening through my 1964 Quad IEMs, my Sony MDR-7506 headphones, and a pair of the church's Westone UE3 IEMs (I think that's the model name - a generic 3-driver model). The J48 sounded fine, I certainly don't go to the trouble of bringing my JDIs with me and swap out the J48. Plus the J48 has more output, which the sound guys like. Still, for sound quality's sake, I still preferred the JDI.
Now.....Having said all of this, I recently played through a Reddi DI. Talk about a massive game-changer!! Since I've been asking around about this DI, I've had touring guys tell me that they did away with the bass mic on their rig because this DI sounded so good. Check it out and start saving your money. The church ordered one last week and I think I'll be playing through it tomorrow night!