To me, it sounds like the difference between rules and principles. Wife wants to live by black and white rules that apply to everyone across the board at all times. It sounds like you are trying to follow principles which can be applied across multiple situations with different outcomes.
Me wanting "inside voices" while her sons (26, 24, 16) play video games.
Her: But remember last year when your team scored at the last second to win the game, you cheered
It sounds like the rule is that if you want inside voices in this situation she wants to turn it into a rule that must be followed by everyone. Since you don't follow that rule, then the rule can't apply to the sons. Is there a way to reframe this? What is it about them being loud playing video games that bothers you? Are there alternative solutions such as having them play in a room where there is a door? Is them being loud interrupting something that you are doing? How often do they get this loud?
Me wanting her kids friends to not walk into our house, but knock and wait for someone to let them in
Her: But remember when we had the party and your sister got here & you yelled "come on in"
I am trying to think of how to frame the difference between these two situations. I think it boils down to whether or not you are expecting guests. If you know somebody is coming over, then it seems like it would be okay if they came on in. However, if you had no prior knowledge of people arriving, that could make for some potentially awkward situations. Is there a compromise that you could propose that would not be so focused on whether or not they walk into the house. For example, could you ask the kids to let you know when somebody is coming.
Me wanting her kids to put their dishes in the dishwasher
Her: You don't always put stuff in the dishwasher.
Would you feel comfortable responding with something like, "you are right. I don't always put stuff in the dishwasher. I would like to see EVERYONE make more of an effort to put their dishes in the dishwasher." That kind of addresses the B/W need to have a rule that applies to everyone.
It combines the typical BPD double standard with everything being viewed as right or wrong instead of a difference of opinion.
I notice that my husband is pretty bound by rules and sometimes has a difficult time with principles, which are the underlying reasons behind the rule. I am not sure if that will help with anything directly but it might give you some ideas of how to think about things differently so you can take a different approach.