I think it is fair to the Haredim to point out that their community has lived in Israel for centuries prior to Zionism and prior to the birth of Israel. Many do not agree with the formation of Israel and Zionism as a country but their were here as a community first and they have stayed and why not? As for the veil; this type of veiling is not new in the region and has been used, as you will see in many artists paintings over the past hundreds of years by Middle Easterners while travelling to keep them comfortable, calm and relaxed and cool. So I would prefer to think that somehow these pilgrims are just going back to some of the "old regional habits." which I am all for, whether they originate with Hebrews or Arabs. If it works impliment it.
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from the article: This year in Uman: Hasids don 'veils' en route to Rabbi Nachman's tomb