TCP786 wrote: Why does the clean feed in Fusion need a LUT?
It doesn't, necessarily. I don't know why it always applies the Managed LUT - almost certainly a bug/mistake.
That said, it is normal and recommended practice to comp in linear, so in practice you'd likely always want a Rec709 or sRGB LUT on all viewers. Even so, the Clean Feed being in the Managed LUT is still a bug I think, because I'm pretty sure that only functions correctly when Resolve is in Color Managed mode.
TCP786 wrote:If a viewer doesn't match because it's not using a LUT, doesn't that mean its input is being changed before it's being output (something I would assume a viewer shouldn't do unless I told it to)?
The Clean Feed viewer didn't match because it WAS using a LUT, when it shouldn't have been. You had the Managed LUT on the Clean Feed, and (I assume) no LUT on the other viewers
TCP786 wrote:And if the Fusion page is missing a LUT application on its clean feed,
What do you mean, missing? The LUT feature is available and working on the Clean Feed - you change it using the method I described earlier. The issue was that it was seemingly turning on the Managed LUT always, even when you weren't in DaVinci Color Managed mode (which is when the Managed LUT is used)
TCP786 wrote:does that mean there's a LUT being used on the viewer everywhere else that I didn't know about?
In Resolve, if you enable Davinci Color Managed mode, then the viewers will default to the Managed LUT. Otherwise Fusion viewers default to no LUT (except the Clean Feed, which appears to apply it regardless), and if you want one you need to turn it on using the LUT button in the top right, or via the right-click context menu. You can then save that as a default for the viewers, if desired.
TCP786 wrote:Most importantly, if there's a LUT conversion happening that I didn't know about, where is it happening in the signal flow of the deliver page's export process?
Nothing. Viewer LUTs are just for viewers. If you want a LUT or colour space conversion in the deliver pipeline, you'd add a LUT or Gamut node. As mentioned you are likely to want a Gamut node for removing the gamma curve of source material (making it linear) prior to comping, then another Gamut node to put it back into Rec709/sRGB at the end.
Here's some tutorials that might clear up a few things for you: