I fly owners & their guests in piston & turboprops in the US now. None of the regalia, just chinos/slacks & a polo shirt. Everything neatly ironed, of course. I've seen similar on many corporate/business aircraft including jets. I've also seen similar but with standard business shirts, and I've seen uniforms. In previous 135/charter/airline jobs it was the whole uniform thing with bars. One of the reasons I chose non-uniform like attire for our little business is to avoid giving the impression that the flights are under Part 135 (they're not).
As long as what you wear is neat and appropriate to the situation, ie not usually jeans & T-shirt stuff, most pax under Part 91 ops won't think twice about it. Your demeanor & how professionally you operate the flight will count more. It doesn't matter how flash the clothing, if your operation comes across as disorganised or tardy, and with things forgotten or not done, then your pax won't be happy.