All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
The income of a person who works in an interest-based bank is, at best, not free from doubtfulness. So if all his income is earned this way, then it is prohibited to engage in financial transactions with him. If he has another source of income that is lawful, then it is not prohibited to engage in financial transactions with him according to many scholars.
Some scholars held that the money earned from working in an interest-based bank is unlawful because of the way in which it is earned, and not because the money itself is unlawful (like stolen money); so it is not prohibited to engage in financial transactions with its earner because the prohibition is related to the earner’s liability only, and not to the money itself.
In any case, it is better to refrain from letting a person who works in an interest-based bank join you in your Udhhiyah unless he is going to join with lawful money. This is better and more prudent in making your offering purer.
Some scholars maintained that in case of purchasing an Udhhiyah jointly, the participants are not all obliged to hold the intention of offering the Udhhiyah and that each share is offered according to the intention of the person offering it. The Kuwaiti Encyclopedia of Fiqh reads:
"The Shaafi‘is and Hanbalis maintained that it is permitted to purchase the sacrificial animal jointly when one of the participants intends to offer his share as Udhhiyah or other intentions of drawing closer to Allah while another participant merely wants its meat, even if the share of the one intending Udhhiyah is one seventh, the share of the one intending Hady (sacrificial animal in Hajj) is one seventh, the share of the one who intends Aqeeqah (sacrificial animal for a newborn baby) is one seventh, and the share of the one who merely wants the meat is the rest of the animal. If the sacrificial animal is slaughtered with these intentions, then it is valid because the action becomes a means to draw closer to Allah with the doer's intention, and not the intention of his partners. If any of the participants who purchased the sacrificial animal jointly fails to hold an intention for his share, then that does not affect the good deeds of the other participants..."
Hence, it can be said that even if the share of the participant who works in an interest-based bank is not accepted by Allah as a valid animal sacrifice, this has no effect on the validity of the shares of the other participants.
Allah knows best.