Suggest U rewrite as:

To prevent the bill from being passed, angry men clamored around the building.

or

the angry men clamored around the building to prevent the bill from being passed

“Being passed” is not an actual or potential attribute of the bill but something that is done to it, consequently you wouldn’t use the genitive (possessive) case “its”.

So I think the correct form is “it being passed” (“it from being passed” may be OK as well, but I am slightly doubtful about it).

BTW in this case there is no problem about any ambiguity concerning whether it is the building or the bill that is in danger of being passed, since it is quite clear from the sentence that it is the bill that is referred to.

“Angry about the bill, the men clamored around the building to prevent its passage.”

Its stronger if you isolate the subordinate clause and unite the subject and predicate…