I suppose you have three goals. (1) Actually be respectful. (2) Show respect in such a way that the other party isn't upset or offended. (3) Do something that constitutes effective collaborative truth-seeking.

If your only goals are #1 and #2 then I think this is easy: if A's and B's notions of showing respect differ, and A knows this, then for A to show respect for B s/he needs to act in the manner B considers respectful.

But presumably you care about #3 too, and in this case it sure seems as if B's notion of respect is actively harmful to the project of finding what's true. I haven't any advice for the general case, but in this case I think the approach you took is a good one. I'd have moved one notch further in the "seek truth even at the cost of possible conflict" direction by asking for more details: What's the actual shape of the taxation curve? At what point does earning more result in lower income tax rates? Do you know why the rules were set that way when almost always the income tax rate is a nondecreasing function of income? (For the avoidance of doubt, I'm proposing questions that assume the other person is correct and seek more information.)

In the UK there is an income-tax-like thing called "National Insurance" that's a fixed fraction of your income between a particular lower bound and a particular upper bound, and then a much smaller fraction of your income above the upper bound. So around that upper bound, it might be true that tax rate is a decreasing function of income. (NI is not formally an income tax; one might cynically suspect that the main reason why it still exists rather than being folded into income tax is that it provides legislators with ways of varying income taxation that don't appear in the headline income tax rates. I think the US social security tax may be similar.)

There's no generally right answer, but I don't think challenge vs. respect is the right model to be using here. Indeed, I feel that the correct response to declarative claims in a given situation usually has nothing to do with the factual correctness of the claim.

Specifically, there are three things that could be going on here. The first is that your friend is making a status play: they're being declarative because they want to assert that they or their tribe have special knowledge, or (rarely) because they want to prove they're cool enough to get you to say that 2+2=5. Usually it's a way of passively elevating the speaker rather than challenging another person; I've found that geeks in particular are liable to interpret surprising claims as challenges, though, because geek self-esteem is often bound up in being the smartest person in the room. This is often a social blunder; actively debating in this case is challenging your friend's status, which is sometimes a good idea but usually isn't.

The second option is that they're making conversation. In this case they don't care too much about the factual content of what they're saying, but social rules differ on how you're expected to respond. Some cultures like gentle, friendly debate; some expect you to graciously accept the information and discard it as irrelevant once you're out of earshot; almost none prefer strenuous disagreement. Debate in this case is not a challenge, but will only be treated as a sign of respect if social conventions allow it. This is probably the most common option.

The final option is that your friend's thinking out loud or trying to solve a problem, i.e. they actually care about factual correctness. This is when it becomes appropriate to fall back on serious questioning if you doubt the information being imparted, although you might have to couch it in more or less rhetorical gingerbread depending on relative status and local social norms. It's also pretty rare.

I think a part of the solution is on how you ask the question. It may feel a bit silly for rationalists like us to put such importance on the form rather than on the content, but for a lot of people (and even to a point, I've to admit, to myself), it's very easy to fall in "group 1" or "group 2" depending how the question is formulated. It may either feel as genuine interest and desire for details, or for an aggressive (questioning trust) move, depending how the exact question is formulated.

As for the main issues, rich people paying lower taxes, when it's the case it's often because rich people have ways to play on various loopholes in the law to avoid paying part of their taxes, or as a negative side-effect from tax incentives. Like here in France, you can deduct from your taxes part of the money you spend in improving heat isolation of your primary home (in order to encourage energy savings) and the combination of many similar schemes makes it possible, at the end of the year, for upper-class or upper-middle class people to pay less in income tax (even if the base rate is highly progressive) than low-middle class people (really poor people don't pay any).

One is to treat the question as a challenge, intended as an insult or indicating a lack of trust. If you have this model of interaction you think people should take your word for things, and feel hurt when they don't.

How does one reason with people like that in general? My usual reaction is to shrug and disengage.

An addendum to [1], social security tax in the US is capped, with the cutoff being around $105k of individual income, so there may be a local dip there in percentage where the increasing income tax doesn't balance the 11% that goes to social security before that point.

What do you want to achieve with your question? Are you genuinely curious about getting the details of the claim or do you have 100% confidence that the person is wrong anyway? Do you expect to gain something from discussing the topic further? It's completely okay that two people have different viewpoints.

You don't need to pretend that you accept it or to disagree to be able to move on. Whenever a topic doesn't seem productive and worth investing further energy you can move on.

What makes facts surprising and is it the same for you and your conversation partner? If they take your question as an insult, you probably have different knowledge of the field in question (they could be completely wrong, or you could be ignorant of something that is well known to some).

I think it's a better idea to explain why you're surprised.

I'm going to borrow from Miss Manners here: it is respectful to treat people as they prefer to be treated. If you know friend doesn't like to have difficult conversations, it is respectful to go by friend's wishes. If you want to probe further, you could put on a puzzled face (lips pressed together, eyebrows slightly furrowed, tilt head slightly, look upwards), and say something in a curious tone. "Huh, that's really strange. How would that happen?" If you sound puzzled and curious rather than defiant, your friends won't take it as a challenge.

Wanted to point out - asking questions may be a sign of respect, but that doesn't mean smiling and nodding is disrespect. Maybe they actually agree with you. ^^ Or if you mean specifically the people who disagree but hide it, there are many reasons a person might not engage in a conversation, and most of them aren't about respect or condescension.

You seem to assume that people endorse the same norm when their claims are questioned and when they question claims. While this assumption is probably true in most cases, it isn't true in others, including my own case. Like you, I interpret a person's act of questioning my claims as a sign of respect. By default, however, I rarely question claims made by other people, since I believe the former norm is more popular than the latter.