Short answer: yes, they can. Regardless of what some websites are saying.
Mastodon is “an alternative to Twitter”. Mashable just wrote that:
“Mastodon.. in many ways it’s like Twitter, but it is also so not like Twitter… What makes it stand out? It has better privacy controls than Twitter. Also, neo-Nazis are explicitly banned.” and then, 2 lines below: “Mastodon is a type of free and open source software (FOSS) known as “GNU social.