Cheapskate on Others' Dime

I've been pondering an issue for quite a while and have been hoping that you readers might be able to add some insight to my dilema.
If you're pinching pennies really tightly to the extent where others look at you and shake their heads in disbelief, should you also keep those same extreme frugal habits when on someone else's dime? I am not talking about taking care with other people's money- of course that is a given, you shouldn't spend wrecklessly with money, even when it isn't coming from your bank account.
However, I'm talking about something a bit more extreme. Frugal lengths to which others would find revolting, strange, or beffudling. Examples that come to mind are:
If you are very stingy with toilet paper, should you also use very little when at other people's homes?
If you never buy expensive dairy products or expensive meat products, but these stuff are givens at other people's homes, is it wrong to allow yourself to "indulge" in this expensive product? (And by indulge, I mean eating more than you would if you were in your own home, but not eating excessive amounts or anything.)
If you never go out to restaurants because they are very overpriced, and when you do go out, you make sure to buy the absolute cheapest thing on the menu, when wealthy relatives are treating you out (relatives to whom even an excessive restaurant bill would be negligible), should you also get the absolute cheapest menu item, or a more regularly priced meal?

I'd definitely appreciate hearing your thoughts on this matter, as I've been unable to come up with a good answer myself.