So I have an expense card for work, which means I am supposed to use that card and only that card (not cash) 99% of the time, basically whenever at all possible, on transactions that are applicable "business/travel expenses." I've run into cash-only taxis once or twice, but it's my understanding that in D.C. and even less metropolitan areas such as Richmond, VA, Square or other credit card readers are commonly used by cab drivers in order to make using a charge card possible. I was actually told there isn't a single cab in DC without a CC reader (truthiness may vary, but it was an attestation from a resident, so it is what it is).
You might live in an area where that isn't the case, but it strikes me as unusual for taxis not to change with the times, and we do live in a digital era now. Square can even let you send/receive cash for free (although I'm pretty sure you aren't supposed to if you are acting as a taxi driver or etc) and it converts your cell phone into a card reader.
POS card charges on vendors are not insignificant, but they're usually pennies on the dollar. While on small transactions that can actually cause a vendor to lose his profit or even lose a few cents (net negative), it's a) the vendor's problem aka the cost of doing business, and b) kind of how things work - you aren't going to make money on every transaction as a person running a business. Unless you have a real reason to care about the person you're paying (like: want to support small business; personally care about them; etc) I don't think it should be a reason not to use your card - but you may feel differently and that's okay. I just kind of feel that it is an expected, known cost of doing business for any and all vendors that enter the money-playing game.
I also have never seen a minimum card transaction requirement at a bar or club, but again, I'm not sure where you are located. For a long time those minimum requirements weren't legal, anyway. They became legal, kind of, As far as I can tell it's only legal for credit cards, due to those aforementioned limits, but where I live that's 2 rum-and-diets and I live in a cheap drinking area. Sure, it's 5 pabst since they're cheap (not including tip) but I'm really not familiar with the scenarios you're describing.
As for entry fee though, yeah, I think it always has to be cash.
I confess I take out money when I need it for a specific purpose and that's the only time I ever have cash usually.