That would require authentication or a keyed RSS feed. This isn't impossible, but it takes some careful consideration and is a possible security issue.

Reddit offers this for some account feeds, using obfuscated, but not authenticated, feeds. If someone gets ahold of the feed URL, however, they have access to private account data.

For Mastodon, a preferred option might be to use a terminal-based / commandline Mastodon client, of which there are several.