The Christian adoption of the he occurred after the legalization of the Church in A.D. 313. Prior to that time, since the Church was an underground movement whose members lived more or less communally out of necessity, the concept of the he would not have made sense -- they regarded all their resources as common to the church.
The Ante-Nicene fathers do not refer to the he specifically, but they do refer to the giving of "firstfruits" to the clergy and to the poor. Several proclaim that the rich are obligated to give more generously than the poor.
It should be noted that both the Hebrew he and the Christian he through medieval times were in kind, since until recent times, farmers and craftsmen made up the bulk of the population.
The practice of the he is not uniform throughout Christendom. Especially in countries where there is no separation of church and state, the church will receive funding from the tax rolls. This is how it is in Russia, and is part of the reason the Russian Orthodox Church is the U.S. is always strapped for cash -- its parishioners are not accustomed to giving.
In some European countries, registered church members are required to pay a tax between 1% and 2.5% of their income to the church. If they want to stop paying the tax, they must pe ion to be removed from the church rolls, in which case they will no longer be allowed to take comminion.
In sum, I cannot say definitively that the he is binding upon Christians. However, it pays to notice that the Southern Baptists, who are just about the most faithful hers out there, can fund several Christian colleges, and have one of the most potent international missions organizations in all of Christendom, while the Orthodox, who are just about the worst, have virtually no profile whatsoever outside of the traditionally Orthodox nations.
I've been in (and subsequently left) a church that squandered millions of dollars of hes and offerings on pointless remodeling. In a church like that which has way too much money to begin with, I don't see the point of giving them the he. Better to send that money directly to missions or to a struggling young church that can use the money. I also question building a 10,000-seat megachurch complex complete with theater seats, a surround-sound A/V system, and a restaurant. But who can argue against the faithful stewardship to resources to promote the spread of the gospel and the discipleship of church members, and to help those in need?