Is the word “classless” neutral in its implication, or does it have a derogatory tone?

Solution 1:

Merriam Webster lists a third sense

3: crass, boorish classless behavior

The article is using it in the third sense. I rarely encounter the word used of a person in a non-insulting way.

Solution 2:

It is being used in a negative sense in that example, but I think the positive sense is also familiar to just about everyone in the English-speaking world from John Lennon's lyrics in Working Class Hero:

And you think you're so clever and classless and free

But you're still fucking peasants as far as I can see

Solution 3:

In the US, classless is usually the opposite of classy, unless strictly dealing with classes in society (which is not the most common use of the word here). Some uses of class:

• "He does everything with class," Blake said. "He answers his questions very carefully, very politically correct, and he doesn't really put himself in a bad situation where he has to try to dig himself out." - NYT, of Donovan McNabb
• ...guys that played on the team with him, you would hear the same statement, that he is a classy guy from top to bottom. - NYT
• It was all plain as day and made its own argument: San Francisco 49ers head coach Jim Harbaugh is a classless thug.

However

• She asks people if Sweden really is a classless society and badgers union officials about why the labor movement is so conservative. NYT