When travelling, managing your contacts with minorities (ethnic or religious) is often problematic.
In many cases, as far as ethnic minorities are concerned, the problem has been somehow solved by the minorities themselves, allowing contact only against payment. The Masai, the Toraja, the inhabitants of the Baliem Valley are just some of the many examples that can be given.
But in the case of Hasidic Jews (ultra-Orthodox) this doesn't happen at all, and therefore contact with them must be managed with the utmost discretion.
This is what we too experienced with the Hassidic people in Me'a She'arim neighborhood: that we crossed during an afternoon for a long stretch in an east-west direction, starting from Ha Shabat square.
We knew that the Hassidic people don't like being the subject of so-called "tourist" attention at all, and we had confirmation of this both through their shy attitude and through a warning present in the neighborhood, stating that to direct group tours here is a heavy offense to their sensitivity.
We therefore tried to maintain as discreet an attitude as possible, hiding ourselves in the crowd (although we certainly couldn't pretend to be Hasidic): which was not difficult, since there were only four of us (two couples).
In this way we could have full experience - among other things - of the particular clothing of the group. However, while we already had experience with the males, having seen them in prayer the day before at the Western wall, we saw the (very discreet) clothing of the females here for the first time.
We also noted the large number of children, which is a widespread goal (families strolling down the street show at least two children, but typically more). Factor which, as far as I understand, makes this segment of the population the poorest among the Jewish population of Jerusalem.
Discreetly we also took pictures; but I only published one, as it hides people's faces.
Overall, I think this is an experience that should be done, practicing discretion.