Is one allowed to hire idolaters, if it is known that part of their salary is donated to idolatrous activities?
Rema Yore Dea 149,4:
אם מפרש בהדיא לעבודת כוכבים שלו או שידוע שהוא לעבודת כוכבים או שאומר לקדש פלוני אסור לקנות ממנו (שם וכן פשוט בתוס' ובהגמי"י)
If the Gentile says explicitely that the money you give him will go towards idolatry, or if it's known he will give proccedings to idolatry or he says "for this idol" you cannot buy it from him
The Shulchan Aruch 149,3 says even if only the tax (i.e a percentage) goes for idolatry it is forbidden to purchase anything from him
אסור מפני שהוא נותן מכס (ואף אם יניחו לו המכס אסור) (טור) והמכס לאלילים
So if he is Selling his services and says even some of procceedings will be given to idolatry you cannot do business with him.
Hiring an idolater to do work for you is the same as purchasing something from an idolatrous merchant. The Sources are full of examples of the latter, which is obviously allowed. So the former is allowed also.
(To be sure, there are restrictions on trade with idolaters around the time of their festivals. They are described in tractate Avodah Zarah (Ch. 1), but they are insignificant in the big picture of trade with idolaters.)