It's been around for a while. The Supreme Court decision that upheld that status was Walz v. Tax Commission—397 U.S. 664 (1970)—and it wasn't a close-run thing: it was 7-1 in favor of continuing the exemption despite the First Amendment's Establishment Clause and despite the implicit tax hike that necessitates on other's land. You can read through the Court's rationale here.

Inter alia, they felt that taxing churches would give the state much more direct involvement with religion and be harmful to First Amendment rights.

Here is a journal article that goes into some of the legal history behind tax exemption for religious institutions. Main points:

There were precedents set in both English common law, and the English law of equity. The reasoning was that religious organisations provided services for the common good, including responsibilities that otherwise would be the burden of the government.

The Wilson Tariff Act of 1894 is the first of a series of statues that formally exempted religious institutions from federal taxes. This kind of exemption is there from the get-to in terms of post-revolutionary taxation law.

/u/uhhhh_no helpfully cites Walz v. Tax Comission from 1970, which upholds these provisions. I'll leave you to read the article for more details on post-1970 developments and the problems of political involvement of religious organisations.

But the main point is that religious organisations in America held tax exempt status from very early on, and the main two streams of reasoning are (a) a development from English Law, (b) consideration of contribution to the common social good.

Thanks!