The API for viewing an instance timeline is public, there are some timeline viewers in the wild [0][1].

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...

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:

https://octodon.social/users/jalefkowit.atom

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.

That's actually one of the reasons (I think) Twitter became popular.

It was easy to quote a tweet, and you didn't need an account.