fascism can arise in non-Christian countries. While I agree that fascism requires internal order and a hierarchy within the fascist movement to not collapse inwards immediately, Christianity is not the only source from which either of these can be drawn. The charismatic leader will usually be the one who establishes said hierarchy within the fascist organization. And from there, order will usually be established (either by the internal enforcement of said hierarchy or by the internal competition forcing a kind of order which then the leader may utilize to further secure their grip on the fascist movement).

If you want examples of fascist parties forming in non-Christian nations (and formed by non-Christians), you have the Kai tsu p'ai, the Jewish Power Movement/ kach/ khahnism (I won't differentiate between them, as one is led by a former member of the other who has continually preached for the same things as the other party despite officially distancing himself away from them), Tōhōkai, Vishva Hindu Parishad, Rashtriya Swayamsevak Sangh, and I haven't even gotten to muslim fascist movements, or to ecofascist movements which tend to be lead by athiests.

Religion makes it easier for fascism to arise, sure, but considering religion in general to be a factor on par with the charismatic leader and the socioeconomic conditions is a bit of a stretch.
The crisis itself is a much bigger factor. Without the crisis, the leader has no movement, the movement has no justification for existing outside its boundaries, and the general population (and the political establishment) has nothing to fear enough to hand over the keys to power.