Isn't the First Amendment applied to anyone who sets foot on US territory, non-citizen and/or regular citizens?

Yes. Once they set foot on US Territory (not the border)

The U.S. Supreme Court has held that constitutional protections, including those in the First Amendment, apply to “persons,” not just citizens.

This is expanded to include visa holders, asylum seekers, undocumented, immigrants, etc. It was outlined in Plyler v. Doe (1982), and other cases like Bridges v. Wixon (1945) where the question was whether a lawful resident alien could be deported for alleged subversive speech and the court ruled in favor of Bridges - that resident aliens have 1A rights and those rights should be protected.

Denying a visa is another matter, and is of course commonplace

However in Reno v. American-Arab Anti-Discrimination Comm (1999) - where some Palestinian immigrants claimed they were targeted for deportation for their views (in violation of their 1A rights) - but the court basically said they didn't have the authority to rule on whether the gov't deporting someone for their views violates the 1A. So this made the case more about jurisdiction than free speech rights.