You can get an Atom feed of any Mastodon user's toots, if you know the right URL format to ask for or have a feed reader that can do autodiscovery. To demonstrate, here's mine:
This means that you can drop a Mastodon user into your feed reader and follow them the way you would follow any feed-enabled web site. No Mastodon account required; in fact, once you know the schema for feed URLs, all you need is their username and you don't need to touch a Mastodon site even once.
To view the local timeline for mathstodon.xyz one can use this link [2], even though [1] looks better (but can't use a direct link).
[0] - http://www.unmung.com/mastoview
[1] - https://m6n-view.hnle.tk/
[2] - http://www.unmung.com/mastoview?url=mathstodon.xyz&view=loca...