What religious communities teach about the Tosefta תוספתא today? I know that among some teachers it is considered legitimate to compare and contrast parallel teachings in the Mishnah, Tosefta, and where possible, the Midrash. Do any Orthodox kollels or yeshivas do so, on any subject? May rabbis today pasken using information from the Tosefta?
It's certainly part of the canon! Rabbi Yechezkel Abramski wrote a commentary on it that you'd find on most yeshiva bookshelves.
The Tosefta certainly features in the halachic process. At this point, though, you wouldn't find a contemporary authority saying "oh the Gemara, Yad HaChazaka, and Shulchan Aruch say it's prohibited -- but I permit it because of the Tosefta!" Earlier authorities had access to it, too.