I only need to set one line in firebase.json file,

{
    "react-native": {
        "crashlytics_debug_enabled": false
    }
}

faced the same in one of my project : "react-native": "0.66.1"

1. Edit AndroidManifest.xml

    <manifest xmlns:android="http://schemas.android.com/apk/res/android"
     package="com.reversedomain">
     <application
       ...
       ...
      // add this line
     <meta-data
     android:name="firebase_crashlytics_collection_enabled"
      android:value="false" />
   
   </application>
   

2. install '@react-native-firebase/crashlytics'

3. add .env at the root of your project & set production = false

4. in app.js

   import React from 'react'
   import { production } from '@env';
   import crashlytics from '@react-native-firebase/crashlytics';
   
   useEffect(()=>{
    if (production == true) {
     // Enable on runtime
    crashlytics().setCrashlyticsCollectionEnabled(true);
   }
   },[])
   

5. docs

The new way to do it, is just add this in your firebase.json

// <project-root>/firebase.json
{
  "react-native": {
    "crashlytics_auto_collection_enabled": false
  }
}

And enable crashlytics collection at runtime:

  if (!__DEV__) {
      crashlytics().setCrashlyticsCollectionEnabled(true)
  }