TYB!
They weren't parasites in the conventional sense.
They were independent and just laid the eggs Inside the people, actually keeping them alive
So IIRC They didn't share anything systemic.
In a sense their life cycle contains parasitic aspects, but just the face huggers wouldn't be.
They respirate on their own, even feeding oxygen straight into the people, and don't extract any nutrients from the hosts.
Pedantic, I know.