There are two basic primary levers in US politics. Money. Votes. That's pretty much it.
If you are able to organize a consistent voting bloc that reliably votes the way you promote, and that bloc swamps all money-based efforts to sway them in any other direction, your voice carries more weight than the money. Period.
Even more terrifying to career politicians is the ability to organize so many voters that you can successfully mount a recall and force the recall on demand; in the US, recall power only rises from local to state level, but does not hold at the federal level, though.
The trick is to continue as that voice, and not step into the ring to play politician. Thus far, no one who was able to organize votes has been able to resist that siren call. That's why vanity is listed as one of the sins. This is also why money steadily overtakes voting power on a long enough time span.
There's at least three: money, votes, and committed foot soldiers (it's easy to think the laaf two are the same, but they don't overlap more than any other pair—whilw commanding votes and commanding people that will work for the cause (and thus move money and other votes) are loosely correlated, they aren't the same thing. One of the particular values form which religious communities are targeted as such is that they often command foot soldiers at a level beyond what is true of groups that deliver similar committed votes.