It's true that it is currently inhabited nearly entirely by Palestinians. However, the important thing is not so much the small (only a few thousand at most) Palestinians who live there as is the area surrounding it.
Directly to the north are a whole bunch of Israeli government buildings (the Ministry of Building and Housing, among others) as well as Jewish neighborhoods up to Route 1. The Green Line is directly to the west. Directly to the East is Mount Scopus and the Hebrew University enclave, which is also internationally recognized as part of Israel.
Directly to the South is the American Colony, Wadi al-Joz, and Bab al-Zahra. However, just south of that is the Old City and Mt. Olives. Israel will not under any conditions be giving up any of the Old City. It's just not in the possible scheme of things. Widespread international sanctions, whatever, will not change that. If the Israeli government agreed to such a plan, it would without a doubt spark a civil war and Palestinians would almost certainly end up driven entirely out of the Old City; this could well end up sparking a World War given what would happen on the Temple Mount in such a situation and how I assume Islamic governments would react.
As such, it is frankly anti-peace for Ir Amim to be saying something like this, since it pushes Palestinians to think they might get a part of it, and since Israeli control of it has no real effect on the viability of a Palestinian state and will not be given up without a fight by Israel, pushing such an idea is harmful to ending the conflict.
These plans complement government efforts to ring the Old City with Jewish development, effectively cut it off from Palestinian areas, unilaterally create an integral population link between the Old city and West Jerusalem and thwart the feasibility of future agreed-upon borders for Jerusalem in the context of a two-state resolution
So, really, Sheikh Jarrah will stay under Israeli control. I would urge its residents to get Israeli citizenship (as East Jerusalem residents, they all have that option; most have deliberately chosen to keep the status somewhat equivalent to the U.S. notion of 'permanent resident/Green card holder') and try to assimilate as best they can; that goes for other Arab Israelis as well. I would urge Jewish Israelis to help them assimilate, and accept them warmly.
Now, as for the land ownership dispute, frankly I'd want to be able to speak and read Arabic and Turkish (or whatever language the Ottomans spoke and used) and frankly have better Hebrew as well, in addition to knowledge on document forgery, plus the ability to personally view the facts before I came to a conclusion, since I don't trust anyone involved.
However, the sentiments espoused by Jerusalem Deputy Mayor Pepe Allalo of Meretz are no less racist than those espoused by the disabled children's parents protest the other day or Avigdor Lieberman or the communal settlements that prohibit non-Jewish residents. At least these ones are:
The issue here is not legal – who does or doesn't own the property. This is an Arab neighborhood in
everyone's opinion and only Palestinians should live here. The residence of Jews here is a provocation and harmful to the calm in the city
Of course, his remarks about the Haredim going wild are right on. Update: I actually went to Sheikh Jarrah in the summer of 2010 and my thoughts on this post no longer reflect my current views.