Is it rude for a waiter or waitress to interrupt conversations at the dining table they are serving?

Mostly, that's a matter of opinion. I think most people would agree that it isn't polite for anyone to interrupt a conversation. However, if a waiter brings food and prepares to pass it out to the customers, the conversation will likely die down so they can get their food. The customers can start talking once they have their food. The waiter should be polite to the customers, but the customers should also be polite to the waiter. After all, it's his job to bring your food and make sure you have what you ordered, even if it means politely letting you know that he's there.