Is it considered derogatory to describe someone as "self-sufficient"?

Solution 1:

A quick and superficial Google-Booking of "self-sufficient" in recent (21st-century) works addressed to broad lay audiences suggests that when the term is applied to individuals rather than states or communities it usually—say three-quarters of the hits—has the economic sense, OED 1b, associated with either achieving economic independence or "living off the grid", and in this sense it's a positive goal.

Use in the sense of emotional or interpersonal independence is neither uniformly negative or uniformly positive. Psychologists and therapists tend to balance acknowledgment of the Maslowian self-actualization project with considerable critique of it:

When you have a sense of strong self-worth, you have a healthy balance between happiness that comes from yourself and happiness that comes from your relationships. Although you’re not totally self-sufficient and happy only to be with yourself, you’re also not dependent on people you’re in relationships with to fulfill you. —S. Renee Smith and Vivian Harte, Self-Esteem for Dummies

About the only domain where "self-sufficiency" has a consistent negative sense these days is Christian theology—for instance this comment on Exodus 32:

Here is a description of a group of people who are self-satisfied and completely self-sufficient. In a word, the celebrants are celebrating themselves. The golden calf at the center of the festivities serves as a mirror that merely reflects back the people’s own image. —Moses Pava, Leading With Meaning

I did however find the negative sense raised in studies of 19th-century literary and political works, like this examination of Meredith:

Nor is individualism the problem in itself, though as we saw with trauma it can become a key site for modern dilemmas over identity. What is a problem, again revealing the centrality of capitalism, is that particular form of it that can be called egoism: the reduction of the other to the status of means to an end, a pursuit of self-gratification as self-realization, and the construction of this as the self-sufficient project of life.—John Jervis, Sympathetic Sentiments

I am irresistibly reminded of Shaw's remark in The Quintessence of Ibsenism that

A man cannot believe in others until he believes in himself; for his conviction of the equal worth of his fellows must be filled by the overflow of his conviction of his own worth.

Off the top of my head (a detailed examination could be the focus of a doctoral dissertation!), I'd suggest that OED's negative sense 2 represents a traditional and conservative valuation whose underlying suppositions were repeatedly challenged by such 'advanced' 19th-century artists and philosophers as Byron, Ibsen, Nietzsche, and Shaw, leading to a largely modern positive valuation.

Solution 2:

In the U.S. at least, the unfavorable sense (2) is old-fashioned. Being self-sufficient nowadays, in the U.S., is a good thing. It's the opposite of being needy.

Solution 3:

Whether self-sufficiency is taken to be a positive or a negative quality will depend on the world view of the individual. There is nothing in the usage of the term in English that implies a value judgement in and of itself.

In many cultures and world views self-sufficiency would be considered extremely admirable. These cultures value independence, hard work and material success.

In other cultures and world views, individuality is equated with selfishness or disregard for the community. In this context, self-sufficiency might be considered a trait to be avoided.

Solution 4:

The emotional sense of self-sufficiency is generally, though not exclusively, used in a positive sense. When not positive, it’s usually either ambiguous, neutral, or as a backhanded compliment (i.e. superficially positive, but (the speaker wishes to imply) on reflection undesirable). Straightforwardly negative use, like in the OED’s examples, seems rare. So it can be used negatively, but its default connotations are positive.

Source: my own general native-speaker experience (which other answerers’ experience seems to agree with), plus searching for relevant uses in newspapers:

If you can learn to love yourself and become emotionally self-sufficient, you'll be much more attractive to other people.

    — The Guardian, Health and Wellbeing, Linda Blair, 17 July 2008

The heroine, and she is one, is a nervy, self-sufficient woman whose sensuous spirit has survived deep insult, betrayal and tragedy.

    — New York Times Books, Her Sense of Snow, Brigit Frase, 10 Dec 2000

It has changed her character, but then it's changed the character of all of us. Our eldest daughter has said to me that it has benefited her in a way, helped her grow up. It's helped all of the children become self-sufficient.

    — The Guardian, A mother lost and found, Kate Hilpern and Steve Chamberlain, 18 September 2010

The closest I could find to the OED’s negative examples:

Codi, who narrates the story, does not imagine that she will actually be able to help her father, partly because of the hopelessness of the disease and partly because of the old man's self-sufficient and emotionally remote habits.

    — New York Times Books, In one small town, the weight of the world, Jane Smiley, September 2 1990

This isn’t a conclusive, rigorous justification — but on a question like this, I think it’s about the best one can do without a fairly involved corpus analysis.