What is the ruling of Islamic law on a sister traveling abroad for study without a mahram, when her family objects in order to prevent her, and how can one reconcile not displeasing the parents with preventing the sister from falling into what Allah has forbidden?

You are correct in your disapproval of your sister's intention to travel for study without a mahram, and in advising your parents against their approval of it, because a woman's travel without a mahram is not permissible except in cases of necessity. Continue to advise gently and kindly, and make supplication. If necessary, seek help from someone who has influence. If you have offered advice and exerted your utmost effort, then you have fulfilled your duty, as Allah, the Most High, says: "O you who have believed, upon you is [the responsibility for] yourselves. Those who have erred will not harm you when you have been guided."