I don't think it's a question of who is ethical or not,
but rather what is ethical. You must understand religious folks find non-religious folks unethical because of their loose beliefs.
On average, they are more commonly opposed to the death penalty, war and discrimination. And they also have fewer objections to foreigners, homosexuals, oral sex and hashish.
Foreigners-
Non-religious: Welcoming, and intrigued
Religious: View them as a threat to their beliefs and numbers. Religious people are obsessed with outnumbering any other type of belief or lifestyle. Therefore in many of the holy texts, mixing of cultures and religious are seen as unethical. This is as a way of preservation.
Homosexuals
Non-religious: Don't really care, accepts any kind of genuine love, so long as a family is provides a nurturing loving environment.
Religious: In the old texts, homosexuality was seen as immoral because it was a waste of seed in the times when the human population was low, birth mortality was higher, and many people were needed to develop the land and replace those lost in the constant wars. All these things are irrelevant now, but religious folks just see it written in their holy books and just agree with it. They would support an abusive family so long as it was a man and a woman, over a gay family, and make other excuses why the straight family is abusive. Point being, Homosexuality is considered unethical under little ground other than, God said so.
Death Penalty
Non-religious: Tap into natural human empathy and compassion with someone. Even if someone has committed a horrible crime (which is usually murder), non-religious take the time to use science to figure out what would drive someone to kill, and use that information to catch potential criminals in the future, or help them over-come the desire to do something crazy. Non-religious folk don't believe in shifting the blame to jinns or demons, just an individual with mental issues that should be evaluated and studied.
Religious: Three reasons
1. If God said a woman must be stoned or beaten, who are we to question? Some of them know deep in their hearts it is wrong but do not dare question it.
2. Also I've noticed religious like the idea of revenge for wrong-doing. The idea of hellfire and suffering for those who were disobedient or did wrong is a sick fantasy of the more fundamental types, and carried over into the mortal world. We were taught, God inflicts pain and punishment if you do not listen or do immoral acts, so religious folks are quick to think that way when it comes to inflicting pain and punishment is ok because God does it.
3. Religious folks see only murder as the most heinous crime that can be committed by another human. Whereas Religions see other acts as equivalent to murder and deserver harsh punishment, such as we all know: apostasy, homosexuality, adultery, are put on the same level as murder, though none of them involves physical pain. Yet, ask yourself why there is little punishment or laws written for, abuse, torture, rape, slavery all of which involved some kind of physical harm to another human being?
Etc. Etc.
In the end it's just what people believe is sinful or not, and we the non-religious folk tolerate and don't care about what we believe are petty things.
Topic: Going Godless: Does Secularism Make People More Ethical?