It is not that a religion purchased the land. I will stay away from any specific current events and focus only on the historical significance of the area.

The reason the area is significant to Jews generally is that Shimon HaTzadik, a Jewish sage, has a grave nearby. The sale was of a plot of land (and the gravesite) that developed into a neighborhood and was known (also) as Shimon HaTzadik, named after the sage. The purchase was alleged to have been from local Arab landowners. The neighborhood was built near the gravesite, on that land purchased by two Jewish trusts, i.e. organizations, not an entire religion. A nearby Arab neighborhood was being built at the same time, namely Sheikh Jarrah, which started to be developed in 1865. As the two grew, they became closer and closer, essentially mingled. Following the 1948 war, and the expulsion of Jews from the Shimon HaTzadik neighborhood by the Jordanian army, the two essentially became one as Palestinian refugees were settled in the now-empty homes of the Shimon HaTzadik neighborhood by Jordan.

I will leave it there. Other aspects of the more recent events post-1967 are incredibly fraught, and still being worked out clearly (both politically and in court), but I wanted to make clear that no one purchased Sheikh Jarrah for an entire religion, and the claim to the plot of land related to a specific neighborhood rests on its purchase in 1875 by two Jewish trusts, who developed that specific neighborhood that intermingled with Sheikh Jarrah over time. The justifications for that claim, the questions of whether Jordan transferred the deed to those Palestinians, how the ownership of all lands lost on both sides of the war in 1948 and after should be handled, and more, I take no position on here, and I want to stress that very clearly.