birdie, I do not adopt Zionism or Judaism by wearing a koppel in Israel when not all Jews would do so. It is a matter of not offending people or, at least, acknowledging their culture. The best course must be to satisfy what is tradition or common. True, it may not be compulsory for Muslims to fast as described (is there a link?) but many do and it is a friendly or diplomatic gesture to follow their practice in their sight. They know that we are not Muslims but will think it pleasing , or not offensive.
Do you stand for foreign national anthems at sporting events? Yes? Then why? If no, do you think ill of those who do? Then why? We are talking of the same principle. It is sometimes called "manners"