I was wondering what others made of that little anthem.
I don't think you can really say if it's major or minor, it's a bit of both, and also you can't really say what key it is in. Starts on an E major chord and moves around, ends on E major.
I think the F# in the key signature could easily not be there, and when I notated this for a choir I had no key signature. It made more sense for reading.
I've seen music from this era notated with one flat, which is definitely in G minor [2 flats].
There's some anthems by Thomas Tomkins which also move all over the place, so one can't really say what key they are in.
Coming back to the original question, Happy Together by the Turtles starts in a minor key, moves to major for the chorus, and finishes in the minor key, ending though on a major chord for the last note.