Cedar fence posts - advantages over pressure treated?
Personal opinion/experience agrees with the advice you are getting. Cedar is a good choice above ground; it's less toxic and as long as it can dry out it resists bugs and weathering pretty well. If the posts will be above ground resting on concrete anchors, cedar is fine. If you are going to bury one end of the posts, though, I would recommend PT. Realistically, the difference in appearance is minimal, especially after staining or weathering. I'd save the cedar for the fence panels.

Of course if you want a natural product that is extremely bug and weather resistant, some of the tropical hardwoods like Ipe are now available for decking and it might be possible to get 5x5 posts. Not cheap, though.