In traditional judaism (not just orthodox) it is forbidden to carry anything outside of an enclosed area on shabbat meaning that one cannot carry an id or their keys. Traditional jews wear a 'shabbat belt' which is essentially an elastic belt that has a hook for keys. The reasoning for this is that the key becomes part of the clothing and therefore the people is not carrying a key but rather wearing it. So umbrellas, not allowed unless one lives in a walled city or a neighborhood with an eruv.
I don't know why they do not use umbrellas . I thought that only meant when in the synagogue to represent the covering of the head as with a prayer shawl. I found the answer the reason they do not use any umbrellas is that the umbrella might break and the umbrella would have to be repaired or replaced and since they do not do any work or transactions concerning money on that day, why would they carry or use anything on the Sabbath. From what I have read. Here is a page to explain further. Hope this helps. Judaism.about.com/od/sabbathdayshabba1/f/sim_shabbike.htm