If you go back to the original Geste of Robin Hood, you see the following:
“Then bespake him Little John
All unto Robin Hood:
‘Master, an ye would dine betimes
It would do you much good.’ Then bespake him good Robin:
‘To dine I have no lest,
Till that I have some bold baron,
Or some uncouth guest,…That may pay for the best,
Or else some knight, or some squièr
That dwelleth here by West.’“…Thereof no force,’ then said Robin;
‘We shall do well enow;
But look ye do no husband harm
That tilleth with his plough.‘No more ye shall no good yeoman
That walketh by green-wood shaw;
Nor yet no knight nor no squièr
That will be a good fellaw.‘These bishops and these archbishops,
Ye shall them beat and bind;
The High Sheriff of Nottingham,
Him hold ye in your mind.”
This is a general anti-authoritarian position: he doesn’t like the clergy, he doesn’t like the royal officials, and he doesn’t like the aristocracy with the exception of those in the lower rakns who uphold the social contract.
However, he’s not anti-religious, he hangs around with Friar Tuck, he’s particularly devoted to the Virgin Mary (which is why he doesn’t kidnap or rob women), etc.