BS”D
So, you honor the social rules of your workplace by wearing a suit – but you disregard social rules which are set down by the Torah community for the sake of honoring Shabbos by giving, let alone attending, a shiur dressed in clothing better suited for a Sunday afternoon spent on a boat or at the golf course.
Think about it. Whose Shabbos are you observing? Yours or Hashem’s? Shabbos is not an American legal holiday or a Sunday off. Sheshes yomim taase melachtecha…shabbos laShem Elokeicho.
By dressing the way you do to give a shiur (and posting here looking for validation of your actions), you clearly make a statement that for you, that shiur is just a leisure activity, not even worthy of the same respect as your mundane six-day work. In other words, for you, melachtecha gets more respect chas vesholom than Hashem Elokeicho.
Is that the message you want to present?
A quick story. Last summer, I had to go to the home center on the other side of town to buy some cleaning fluid or another. It was hot, and those solvent bottles sometimes leak as they are crummy local stuff, poorly packaged and labeled. I was debating whether to wear a jacket and decent slacks or to go in a torn shirt and house pants. I chose the former, keeping my tzitzis out as I would at any other time.
I stopped in front of a display shelf for a few minutes to decide what to buy, and sure enough I heard a well behaved boy ask his clearly educated mother, just out of curiosity and with no malice whatsoever: “Mama, is he a Jew?” The mother, not sure whether I would be insulted (remember this is Ukraine and even the proper word for Jew was chas vesholom considered just about an insult during Czarist and Soviet times), quietly answered yes. And I held my head high as I nodded and smiled to let the mother know that I am very happy for her and her son to identify me as a Jew.
Now, how would I have felt, and how would that kid have thought of Jews, if I had wearing a torn shirt and a pair of pants I wear to fix the plumbing? (Maybe this one should be in hashgocho protis, as it seemed clear to me that Hashem was sending me a message that I am right to always look like the Jew who I am proud to be.)
And remember now, this was the equivalent of Home Depot on a hot summer weekday, not shul on Shabbos Koidesh.