Fugitive respects status.showUntrackedFiles and provides gI for low effort ignoring. These are Git's solutions to untracked files, I don't think we need to invent new ones.

Given that it uses foldmethod=syntax the change for this is rather trivial - happy to keep it locally, but you might want to consider it:

diff --git i/syntax/fugitive.vim w/syntax/fugitive.vim
index afc0c0b..9f7322d 100644
--- i/syntax/fugitive.vim
+++ w/syntax/fugitive.vim
@@ -26,7 +26,12 @@ syn match fugitiveHash /\<\x\{4,\}\>/ contained
 syn region fugitiveHunk start=/^\%(@@\+ -\)\@=/ end=/^\%([A-Za-z?@]\|$\)\@=/ contains=@fugitiveDiff containedin=@fugitiveSection fold
 
 for s:section in ['Untracked', 'Unstaged', 'Staged']
-  exe 'syn region fugitive' . s:section . 'Section start=/^\%(' . s:section . ' .*(\d\+)$\)\@=/ contains=fugitive' . s:section . 'Heading end=/^$/'
+  if s:section ==# 'Untracked'
+    let fold = ' fold'
+  else
+    let fold = ''
+  endif
+  exe 'syn region fugitive' . s:section . 'Section start=/^\%(' . s:section . ' .*(\d\+)$\)\@=/ contains=fugitive' . s:section . 'Heading end=/^$/'.fold
   exe 'syn match fugitive' . s:section . 'Modifier /^[MADRCU?] / contained containedin=fugitive' . s:section . 'Section'
   exe 'syn cluster fugitiveSection add=fugitive' . s:section . 'Section'
   exe 'syn match fugitive' . s:section . 'Heading /^[A-Z][a-z][^:]*\ze (\d\+)$/ contains=fugitivePreposition contained nextgroup=fugitiveCount skipwhite'

(only used it for Untracked to not mess with inline diffs (with would need to be opened then otherwise automatically (with = etc))

As for my use case: I want to be aware of untracked files in vim-fugitive (rules out status.showUntrackedFiles = "no"), and I also do not want to ignore them (always).
In the shell I use gst with --untracked-files=no, but also have gstu to show them.

Since I have a huge number of them in some repos, this is rather distracting then in vim-fugitive.

Being able to zc them is nice. I might even end up closing the "Untracked" fold then by default.
(I've some special processing for filetype=gitcommit buffers already, where those and unstaged files get folded away already (with git commit -v), so I am used to this kind)

JFI: I am not a heavy user of :Gstatus, but getting my toes wet - due to all the recent niceties there. Thanks a lot! :)

So the section you want folded gets a fold attribute, but the others don't? Hard pass.

It's because other sections use inline diffs:

(only used it for Untracked to not mess with inline diffs (with would need to be opened then otherwise automatically (with = etc))

It might work better in general if = would also use folds in the first place, i.e. have an intermediate fold level then for the files, and configuring foldlevel to automatically open diffs then by default etc.
=> #1356

@blueyed you still using this solution locally? I'm also interested in folding away Untracked as a couple projects I work on generate many artifacts upon make test that aren't tracked/explicitly-ignored (I know, not ideal, but out of my control).

I see the PR open (#1356) but it doesn't look like it's had activity in a bit, wondering if it still works well for you

I just removed automatically enabled folding in the status window. Assuming that doesn't ruffle too many feathers then I am fine to add the extra level section of folding since it will only affect those who opt in.

But we should probably make all sections foldable, including Rebasing, Unpulled, and Unpushed.