As always, #your headcanon may vary, but from my own reading of the books and the characters focused on (the main coven), AR does not make it clear how much power the vampires have in the world* beyond the fact that they’re rich if they want to be (like Armand and Daniel owning and running the luxurious Night Island, a lucrative hotel/entertainment/casino/art-space/etc.), or not (Louis living in a dilapidated shack w/ few physical possessions).  

Santino and the Children of Darkness might have had some impact with their religious zealotry, but targeted at the world in more of a negative way, a League of Shadows sort of group. Other vampires, especially the new ones introduced in PL, we don’t know much about their interest in economic or political influence.

Speaking of Louis… 

he put the Coven of the Articulate’s stance very eloquently in QOTD (my emphasis added):  

[^Louis by @remarried]

“It’s their world, not ours,” he said humbly. “Surely we forfeited it when we lost our mortality. We have no
right now to interrupt their struggle. If we do we rob them of victories that have cost them too much! Even in
the last hundred years their progress has been miraculous; they have righted wrongs that mankind thought
were inevitable; they have for the first time developed a concept of the true family of man.

… Don’t interfere with them.
Even if they kill each other! Give them time to see this new vision realized; give the cities of the West,
corrupt as they may be, time to take their ideals to a suffering and blighted world.“ 

Cut for length, not spoilers.

*That was the issue that was brought up in QOTD, whether they had a responsibility to have political power and/or have influence the world or not. There was a council of sorts, and some heavy debate was had, mainly on the part of Lestat’s ultra feminist SJW girlfriend vs. literally everyone else except Lestat who mostly sat there terrified into silence and not taking sides, and it ended with the general agreement that they shouldn’t meddle in mortal affairs.

This is partly bc writing their involvement into actual historical events could be difficult if not impossible (What, did they fight in WWII? Which side? How would that even work, concealing their vampirism from their fellow soldiers??!), and partly bc AR herself wasn’t very political back in earlier canon.

Even now, in the later books, AR keeps her world mostly separate from the Real World; IIRC, Hurricane Katrina was never mentioned in canon, and one would think that NOLA-branch coven founders Louis and Lestat would at least comment on that obviously devastating tragedy. At least one fanfic writer did take up the challenge of weaving in Katrina, and did it very tastefully. So it’s possible, but AR hasn’t gone there.