What did the Rebbe say about wearing contact lenses?
In this link, Rabbi Label Groner says that he heard on many occasions from the Rebbe that he does not allow people who ask him about wearing contacts to wear them in any conditions even for a short time. The Rebbe explained that it is a danger, both hard and soft contacts.
In Mind Over Matter, p. 344:
The Rebbe’s secretary, Rabbi Leibel Groner, relates that the Rebbe refused to use contact lenses. Similarly, he responded to several Chabad women and girls: “It’s not worthwhile.” “Don’t use them (if possible).” “My opinion against using them is well known.” According to Rabbi Groner, the Rebbe did not seem to differentiate between “soft” or “hard” lenses. If the Rebbe ever gave approval at all, it was rare. One of the Rebbe’s secretaries related that he was once present at a discussion between the Rebbe and a renowned ophthalmologist. The doctor discussed a patient of his, a woman who had serious eye problems, and whose only hope (in the doctor’s opinion) to assure her continued sight was through contact lenses. Despite all of his explanations, etc., the Rebbe responded: “You will not succeed in getting approval from me. In my opinion, it is not worthwhile for her to use lenses.” Obviously, when the patient heard that the Rebbe disapproved, she rejected the notion, and her eyesight improved without them. On another occasion, the Rebbe showed that same secretary a report from an Israeli newspaper where they wrote about two cases where medical problems were caused by the use of contact lenses. After the secretary read the report, the Rebbe said: “From this you can see that I am correct in my objections.” (Mind over Matter).
Note that there are many secular studies available online about serious risks over contact lenses, particularly among children and teenagers.
See also here.
Nonetheless, there are cases where the Rebbe gave some level of approval, such as כעצת רופא ידיד, following the advice of a doctor who is a friend, or the Rebbe referred to a Rav. See here for a manuscript of the Rebbe, where he referred a woman who wanted permission to wear contact lenses only on Shabbos to ask a Halachic question by a Rav.