Is there a professional etiquette regarding jackets in academia?
I don't know if I'd call it an etiquette, but there are certainly different ways to dress in different subfields of disciplines. If you attend an academic conference and notice such things you will see the variety by clique. As for tweed, my partner and I wore it as students (bought second-hand in Edinburgh) and we were mostly viewed as the eccentrics we are, as far as I know. Dressing decently generally shows respect for others, though a few people find it an affront to their class consciousness. Dressing expensively can be seen as distancing from those who can't afford it. The main thing is to be confident that you are presenting yourself as who you really are, so then if there are any concerns you can hopefully laugh them off or explain your dress as a matter of personal taste and/or a concern for general aesthetics.