What is the ruling on using, modifying, and publishing content or programs that are subject to "free" licenses, which impose legal conditions that may not include Sharia controls, and is adherence to these conditions considered seeking judgment from other than the law of Allah?

There is no objection to using licenses and programs that contain conditions contrary to Sharia if no alternative is available, because these conditions have become widespread, and prohibiting their use would cause people hardship and difficulty. A Muslim must intend, when using them, to affirm what is permissible and not what is forbidden. There is no difference between using them as they are or modifying a work and publishing it under them.