With modern cameras and probably more importantly, modern post processing software, ISO values that I would have never dreamed of in the past can produce more than just "keeper" images but rather good ones. I like this one and feel that it shows good color and detail rendition. This is a Streak-chested Antpitta, shot in the rain forest of Panama. This was early in the morning (when these birds are active), and deep in the undercover. The RAW file was converted in DXO Pure RAW 3, processed in PS (BG down, bird up in brightness and saturation) and finally run through Topaz De Noise at very low settings (noise reduction at 8 and sharpness at 10) prior to JPEG conversion. Shot with a Canon R5, 600 f4.0, SS 1/800, f/4.0, ISO 16,000, handheld.

If people want to wing it on white balance it is not the end of the world, and modern cameras often get you close.
Personal pictures are just that, and if they are happy with the result, there is no problem.
We all do that from time to time.
If you do work for others, a higher standard than guessing at what you remember is probably a good Idea.
This is especially true because it is generally as easy as the OP placing a card in the scene to get a base white balance.
For your church pictures, at a minimum , before or after services while the lights are still on make an exposure of your card in each lighting area, make notes, then you know.
It is not really true that any white fabric or surface will give a good reading. Many fabrics & paints use optical brighteners with a strong UV component. There are many truly neutral white and gray cards that can work, and they are easy to keep in your bag. The Calibrate/X-Rite little color checker works well.
If you do use a gray card, be aware that Gray cards made for film were not neutral- and were meant for exposure only. In color science there is a whole scale for neutral Grays called the Musnell Gray scale.
But also, not all photographs NEED to be color accurate because Pleasing Color is sometimes more important.
We all make photographs where we want color to recreate how we felt in the moment.
BUT.....
Some work needs to be color accurate, and in those cases it should be.
When I did Product photography, I always provided the client with one test photo with (the original Macbeth Color Checker) the target included. Because they could use that with the printer who printed boxes or anyone else in the chain. My Wife & Daughter shoot Weddings and the clients are very particular about the color of the Brides maids dresses . Architectural Photography is another, getting skin tone just right in portraits, another Being able to match color is just part of the job in those cases. Pros scout locations and do test shots ALL the time.
So there is never one right way to do Photography, but some pictures need to be objectively accurate.
How accurate is up to you (and the client if there is one).
There is one last issue, and that is consistency of look in a group of pictures that will be displayed or published together. The only way to do that and make it repeatable, is to have some form of reference.
I hope this helps a bit

While I understand UserID's perspective, your job is to produce a recognizable and identifiable reproduction of what the congregation has seen or will see when sitting in the pews. Unfortunately, you cannot use your recollection of what you think you saw in this situation, because your brain will do all sorts of mysterious adjustments to make sense of what it thinks it sees. You also cannot rely on your camera's Auto ISO system, because it will fall prey to the same tricks and confusion.

What I've learned to do over many years of photographing all sorts of staged events, is to focus on the main speaker (or singer or performer) and ignore everything else. This person can almost always be counted on to be in light that is at least supposed to be white. If you can learn the base Kelvin temperature of the lighting, set to that. If not, and if it's an LED system, 4000K is a good starting point. 3200K can be a starting point for incandescent, but I've had to go as low as 2700K for some older systems.

Bottom line...focus on the speaker, ignore everything else. And don't allow WB to change while you are shooting.