No to the first, depends to the second. For the first:
You can be proud of your own culture while understanding that other cultures have different values, but ethnocentrism takes things a step further, into the realm of judgment. It's hard to say that 'My culture is better' while at the same time understanding that 'better' is subjective.
(Note that I'm separating moral relativism from cultural relativism here.)
As for the second, what msg_v2*, Qlip, and Hard said. It's entirely possible to argue that certain cultures are better at certain things than other cultures, and you might even reach some degree of objectivity if you get specific enough. Like I might argue that American culture is good at absorbing foreign recipes, giving them a deliciously unhealthy spin, and then mass-producing and selling the end product. I can already see a few ambiguities and weak spots in my argument, but with enough refinement I could argue it.
*With the exception of msg_v2's comment about nihilism, which I may or may not quibble about later.