Are there evil acts which are not sins?

Wow, this is an excellent question.

In essence, there are some things that are unethical from the viewpoints of some societies that are not immoral. Polygamy and slavery are two examples of this. However, anything that is immoral is, by definition, a sin.

Definitions

There are two approaches I can see to answering this question. And these two appraoches really boil down to two definitions of "evil".

Dictionary.com on evil

1. morally wrong or bad; immoral; wicked
2. harmful; injurious

If you come from the direction of "evil" meaning "morally wrong or bad" or "immoral", then the very definition of "evil" implies that something goes against God. In this sense, the question becomes tautology and is merely asking the definition of a word.

However, there are acts that some people consider "evil" that others do not consider a evil. This is the second perspective (from the second definition listed above): the perspective that "evil" is something that is harmful. And this argument boils down to ethics.

So, the question is (from this second perspective): is there anything that is "evil" (in the sense that it is not ethical) that is not a "sin" (in that it is not immoral).

For that, I need to clarify two words. For our purposes, please accept these definitions:

Unethical

unwilling to adhere to proper rules of conduct for the given society

Immoral

violating principles guiding the distinction of good and bad

_{Support for these definitions can be found here: [1], [2], and especially [3].}

Distinction

While the distinction is very academic, it's actually critical for the understanding of how something can be "evil" without being a sin. So, I continue...

The essence of these two definitions is that something is "unethical" if it violates what society accepts as normal, acceptable behavior. Because of this, something that violates ethics of one culture (and therefore be considered "evil") may not violate the ethics of another. By contrast, an act is considered "immoral" if it violates the sense of what is right and wrong (good and evil).

Even in this sense, immorality is a sin. In fact, immorality is the definition of sin. Since God has laid down what is right and wrong, good and evil, we know without a doubt what is sin and what isn't. Determining whether something is moral or immoral is exactly the same as determining whether something is a sin or not.

Contrast

So, can something be "evil" in the sense that it's unethical and still be moral? To answer this, we need to find something that may be considered harmful in one society (and therefore "evil") while it's considered normal and acceptable in another--all while being allowed by God (and therefore moral).

For that, I point to three examples: polygamy, slavery, and garments.

Looking at our first example, polygamy has been an acceptable part of societies throughout history. In fact, the vast majority of known societies have been polygamous (source). And there are societies that are both Christian and polygamous (Kenya, for example 1 2). Because of this, we can see that polygamy is a value that has been accepted by some societies and not others. It is, therefore ethical in some societies and not in others. However, since there is no solid biblical basis for declaring polygamy immoral, it remains moral, but unethical.

Our second example, slavery, follows the same reasoning. I'll leave those explanations to these sources: [1], [2], and [3]. Essentially, though, it's been viewed as "evil" by societies that do not accept it and acceptable within societies that do accept it, making it an ethic, rather than a moral.

I won't site any sources for this one, but rather appeal to the common sense: In many cultures, wearing certain garments is considered "evil" (such as wearing a bikini in Iran or women being topless in the United States). However, other societies find these completely acceptable and normal. Because of this, these societies may find wearing certain clothing "evil", although it violates no sin (per Christianity).

Summary

So, to answer your question: If something is immoral, it is by definition a sin. If something is unethical, however, it may or may not be a sin. Usually, however, it is.

Since sin is in essence any act of disobedience towards God or disbelief and we know that God is good¹ we can conclude that there are no evil acts which are not sins.

¹In fact good and evil are defined by and measured against His nature.