Apollo and its developer take your privacy very seriously. Apollo does not sell or rent your data, and anonymous information is only collected to help make the app better. If you want a privacy-first app for Reddit, Apollo is a very safe bet.
When signing into Apollo, it requests specific permissions from your Reddit account, such as the ability to upvote. This is very simply because in order for Apollo to do anything — something as simple as upvoting a link when you tap the upvote button — Reddit (rightly) requests that you give the client the ability to do these things. Apollo never performs any actions without you clearly requesting it to (such as by tapping a button). This is very simply required in order for the app to function whatsoever.
Apollo (obviously) uses the Reddit API to function, therefore Reddit is able to see requests made and use that information (such as, as with all Internet requests, your IP address, and if you sign in to Reddit within Apollo, your account ID, for instance) as they see fit (for advertising or something of the like, as an example). By using Apollo, you're (obviously) subject to Reddit's Privacy Policy as well as any other services/websites you visit/encounter/use within the app.
For crash reporting Apollo uses Bugsnag and for basic analytics, Apollo uses Mixpanel. This is purely to be able to catch crashes so I can fix them, and collect some information that can help me make better development decisions for Apollo, for instance by knowing which percent of people use dark mode versus light mode, if a feature is being used a lot, that kinda thing. You're completely free to turn off crash reporting and analytics entirely via Settings tab > About > Crash Reports & Analytics
For push notifications (inbox alerts, subreddit watchers, trending posts), your OAuth token is synced between Apollo (the app) as well as the server. The server only stores enough information to function, which includes the ID of the most recent inbox item (if inbox alerts are enabled, so it knows not to send anything from that point or earlier), plus your Reddit account ID(s) and the Apple Push Notification Service token (an ID for the iOS or Mac device that Apollo sends notifications to so Apple can deliver them), and if you have subreddit watchers or trending posts enabled the server will add those subreddits to your account info so it knows to search for them and notify you. Removing this is simple, if you remove your account from the app it will be erased from the server. Otherwise if you delete the app upon sending the next notification the server will receive an error that the device is now unreachable and it will delete it 30 days from that point (to allow a grace period in case you just toggled off notifications temporarily, for instance).
Apollo also uses the YouTube API Services in order to provide functionality such as loading thumbnails for YouTube videos. As such use of YouTube (and other Google services) are covered by the Google Privacy Policy and YouTube Terms of Service. Apollo does not collect or store YouTube data and user information, nor does Apollo permit you to sign into YouTube, so there's no YouTube user account information to be accessed.
If you have questions or concerns about any of the above please contact contact@apolloapp.io