It is a minhag in Chabad to only eat vegetables that you can peel on Pesach. There is a possibility that either the wax coating on certain vegetables contains chometz or that certain processing of the vegetables contains chometz. Without discussing the validity of this minhag, the question is do other groups outside of Chabad follow this chumra?
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This is not a practice unique to Chabad, and did not even originate with Chabad.
The Nitei Gavriel (Pesach vol 2, chapter 39, paragraph 14) mentions this custom, saying that "Many are stringent on Pesach to only eat peeled vegetables".
In the footnote he references the Chayei Adam 127:2 (not a Chabad source) and Orchot Chayim Lifshitz (notes to Orach Chayim 447) (I don't know enough about him to know his Chassidic affiliations).
Both those sources say that if we are worried that dried fruits may have some flour/chometz on them, we should also worry about peels.
If we are certain that there is no way chometz came in contact with them, we may eat the dried fruit. If we're learning that one should peel fruits and vegetables from dried fruits, it would stand to reason that if one is certain chometz did not come in contact with the fruit or vegetable (e.g. they are home grown, and the grower was careful not to bring chometz near the fruit), one need not peel them.
I know of Satmar, Bobov, Belz who also only eat peeled fruit and vegetables on Pesach.
In Breslev we wash fruits and vegetables thoroughly. If one is concerned about chometz in the coating, they consult their Rov. Speaking for myself, it's not something I concern myself with.