The big example in my mind was art made because of and through the Catholic Church for like a millennia or so. It's function in spreading the religion, encoding meaning, etc. Still some incredible and beautiful art in some cases in my opinion.
Consider also things that we tend to classify as "crafts": knitting, sewing, embroidery. These things used to be/are rich with traditional and deterministically cultural-political meaning, but still can be beautiful--certainly pieces of art IMO.
In all these cases, there are certainly particular artists with certain abilities and feelings behind each particular instance, but that is only a sufficient, not necessary, quality to them being works of art I think. It's at least not as important as the fact that Van Gogh did Starry Night.
Edit: almost forgot a huge one: folk music!