"Red flags" don't mean things will crash in the case of Banished mods. Mods are marked as "incompatible" when they touch the same files. When several mods alter the same file, only the one loaded above the others will have any effect in game.

That means that you can have CC and mods designed to change things in CC (like storage size tuning mods made especially for CC) showing as "incompatible" when in fact they work well together and were indeed made to work together. As CC is a huge mod and touches many aspects of the game, it will show a conflict with most other mods. You just need to think about your loading order.

One thing you really need to keep an eye on is the release date of the mods. The last Banished update (1.0.7) added some extra materials categories, limits, flags, so old mods that touch items or alter the category items fall in (or old storage/trading mods) that were made with the older version of the modkit, before those extra flags were added will have a high risk of crashing.

I'd recommend trying CC only first, and then having a look at what's in it, versus what the other mods you wanted to install add, and checking what you really need. And then thinking about whether it's a mod that will use things that come from CC (load under) or that will tune things added by CC (load above CC).

And in case of doubt, you can ask here about specific mod, and with some luck someone who uses both can answer :)

As it happens, CC Journey actually does what nearly all the other mods I had downloaded do so it's not that big of a deal. Thank you for the information, though. That's very good to know going forward.