I have never presented a written-out and formal taxonomy of the Right so far - but reflecting on Bonald's more complex taxonomy which I posted two days ago makes me realise I implicitly use a simpler (and more simplistic) threefold taxonomy as follows:
1. 'Mainstream' (or pseudo) Right (which is actually part of the Left)
2. 'Fascist'/ commonsense Right - which is the secular anti-Left, a reaction against the Left
3. the Religious Right - which is pre-Left: it is what the Left was/ is reacting against.
So the chronological order, and causal sequence, is as follows:
First there was the Religious Right, and nothing else
Secondly there was the Left which was a reaction against the Religious Right, therefore Leftism = the anti-Religious Right (and includes the pseudo-Right, such as mainstream Conservatives and Republicans, and libertarianism).
NB: The Left is intrinsically and necessarily anti-Religious, although secularization of the Left was gradual, and remains incomplete except among the elite politically correct intellectuals. Insofar as a person or institution is Leftist, by that much they are anti-Religious (which is compatible with a relatively high level of religiousness, nonetheless; especially in a society where the average level of religiousness is low).
Thirdly there was Fascism which is Secular Commonsense anti-Leftism, therefore Fascism = the Non-Religious anti-Left.
And that's it!