Any mode or scale can be built on any tonic.
So, yes, you can have
D mixolydian... or
D flat mixolydian,
C mixolydian, etc. etc.
If you have analyzed the song to have a
D tonic and is mixolydian in mode, then you can say it's in
D mixolydian. It's good that you analyzed for what is the tonic, then the mode. That's analyzing tonality. Simply seeing all the chords fit into a key signature of one sharp... therefore it's in
G major, is not the way to analyze tonality.
Keep in mind lots of music changes mode and/or changes tonic. It common for music to shift back forth between modal and tonal harmony. Greensleeves in an example where the harmony is modal in some parts
Em D Em and tonal in others
B7 Em. Lots of music labelled "modal" does that kind of thing. The "modal" music of the Renaissance did that kind of thing. Even if the Clapton song had a
A7 D in it, you might still call it "modal" if you felt there was enough modal harmony to justify it. There is no strict cut off for what to consider modal.
Rock music is so heavily flavored with the mixolydian mode, especially from the
♭VII chord, it's hardly worth applying that modal label to most rock harmony. Rock melody is often very pentatonic and so omits certain degrees which would otherwise make specific modes clear.
This Clapton song is interesting on both points. It does have a
♭VII chord, but additionally is uses a minor
v rather than a major dominant. Melodically, in the verses, it is not omitting the seventh scale degree - which happens in a lot of rock music - instead it emphasizes the
♭^7 degree. However, in the chorus, at the conclusion (cadence) of the line "let your love rain down on me," the melody does skip over the seventh degree. If one were to put a
A7 D move in this song, that would have been an obvious place to put it.
Most people would probably simply say it's in
D. You could make a case for calling it mixolydian. I would understand why. If you called it
D major, I would say "hold on, not like Mozart D major."