S.H.I.E.L.D. likely classifies Asgardians as aliens, judging by this dialogue from an early episode of Agents of S.H.I.E.L.D.:.
SKYE: So, Asgardians are aliens from another planet that visited us thousands of years ago?
AGENT COULSON: Or more.
SKYE: And because we couldn't understand aliens, we thought they were gods? They pass by May, testing an artifact on the floor.
AGENT COULSON: That's where our Norse mythology comes from.
SKYE: [sighs] That's too crazy. Do you think other deities are aliens, too? Vishnu for sure, right?
Agents of S.H.I.E.L.D. - S01E08 - "The Well"
Odin probably would've agreed with this classification, since he clearly stated that MCU Asgardians aren't gods.
LOKI: I went down to Midgard to rule the people of Earth as a benevolent god. Just like you.
ODIN: We are not gods. We are born, we live, we die. Just as humans do.
LOKI: Give or take 5000 years.
Thor: The Dark World (2013)