@Kecessa speaks unclearly when saying “public space”—the term they are thinking of is usually “public forum.” source
The rules around what constitutes a true public forum and what the public forum doctrine even means are fuzzy, but in all cases the term refers to a space owned or created by the government.
Thus, a shopping mall, parking lot, or internet forum, being owned by a private company, is not a public forum and can’t really be defended on the basis of the public forum doctrine.