Simple change to first paragraph of chapter cause other paragraphs "re-compose". How do I stop this?

This kind of a "reflow" isn't a big deal - you just need to create PDF from the original file - for reference - then manually fix those lines - either by compressing or expanding your text slightly - there shouldn't be too many of them.

I think that maybe you are digging in the wrong spot. The composer is actually a paragraph-level setting, not a document-level setting, so changing the composer on one paragraph should not affect downstream paragraphs. 

However, one thing that will cause recomposition throughout a story is to edit it in a version of InDesign that is later than the version in which it was created. So: let's say you did the index in InDesign 2022, version 18.3. Then you upgraded to InDesign 2023, version 19.0. Then you open you y indexed document.

 our text boxes will still look like they did in 18.3 until you make a text edit in one. At that point it will recompose the entire story. If the text composition rules have changed, and you have a line that just barely fits, then there is a non-zero chance of reflow.

You can force the issue by using the Recompose All Stories shortcut, which on Windows is  ctrl-alt-/. That will show you all the places you need to redo the copy-fitting if you don't want to redo the index 

The real solution is to never upgrade a document in the middle of a project. You can install the latest version of Indy and keep the old version installed. So that way you can do your new project in the latest version, but you don't have to upgrade your months-long project, which can induce all kinds of problems when you upgrade.

If you wrote over your old version of InDesign, you can reinstall it from Creative Cloud; there is a little drop down next to the Install button that lets you install older versions.

Coming back to your question 'Is there a way shut off the “recomposition” feature?' -- No, there isn't. When you touch some text in InDesign, its parent story recomposes. There's nothing you can do about that. Composer type has no influence on that. The single-line composer may sometimes absorb recomposition, but recomposition happens nevertheless.

Steve's answer probably addresses your immediate question, but let me add —

Non-indented first paragraphs, at the start of chapters and following any heading or column break (space, or a separator glyph) are pretty standard for page composition. I'd make it a habit to do layout that way. The proper way is a child paragraph style: Body as a basis for Body NoInd, for example. If you're implying that you're doing it some other way — with spot formatting of those paragraphs, for example — yikes, stop that. Always use styles.

Assigning a style to these lead paragraphs can let you fix any consequential problems, too. The only reason I can think that "other paragraphs are recomposing" is that you're inflicting an unwanted style change with the indent fix — and a separate, child style should prevent that — or that you have first paragraphs that lose a line because of the indent space going away. If the latter is the case, you could tweak the spread of those paragraphs by a tiny bit to make up for the lost space and make them wrap to the same number of lines. (And that's why you "always use styles!")

You also say it's a problem because "the book has already been indexed." In a tool like InDesign, if the indexing is done with inserted anchors, it should be trivial to update the index after any change to the content. If you're manually maintaining an index... that's a lot of work that can be avoided by using the tools already at hand.

The default Adobe Paragraph Composer purposely tries to recompose lines to produce the best spacing for the type.

If you want only individual lines to be affected during composition, choose Adobe Single-Line Composer from the Control Panel menu: