Is it Ethical to Own Shares in an Unethical Business?

Not always, but I think it can be. As a small, independent investor, your ownership of the business generally will have very little impact on that businesses' future decision making, or stock price, or worth, or reputation. So, the consequence of your ownership rests largely with the consequences of how you spend your profits.

As a larger investor, you can influence the actions of the business in certain circumstances, allowing yourself to improve the ethics of the business.

Of course, this line of thinking relies on the basis of the business' ethics being a seldom prioritized value, and there can be cases where even small ownership is a considerable boon for a company. However, the case of share ownership ethics is never as straight-forward as many think it to be; owning shares in a tobacco company, for instance, can be the best way to fight the ill-effects of smoking.