I thought about this one for a good while. Frankly this isn't a Yes or No question, which is true of most if not all philosophical debates.
My personal view on this question focuses on "Dependent" being the keyword. According to Oxford Reference "In theoretical frameworks, an independent variable is a phenomenon that is seen as influencing the behaviour of some other (dependent) factor." In context of the question we are asked. Is religion a phenomenon that is seen as influencing the behavior of ethics? Framing the question this way all we need to do is assess if religion influences how ethics behave. My own definition of ethics is either a spoken or unspoken moral code that is personal, regional, or universal. In essence ethics are the physical embodiment and observance of our moral codes. Moral codes themselves can be created from secular sources. If we look at North Eastern countries such as Russia, China, and North Korea. We can see a strict sense of secularism with little religious observance. Yet, these communities do have their own moral codes which are influenced by the governing body. However even Communism is influenced by religion. Marx took great pains to explicitly note the moral shortcomings of religious bodies such as the Catholic and Lutheran churches. He went so far as to convey the idea that the class system and the poor state of the proletariat was a direct result of these faith systems, empowering the rich and trampling on the poor. As a result Marxism or Communism is a moral code whose ethics and beliefs strictly avoid religion. That is proof that even the most secular groups are created due to the influence of religion. Based on this I would state agree that ethics are dependent on religion, in that they are influenced by religion. They can and do exist outside of religious organizations, but that does not mean that they are independent of religions influence.
There is a subjective or psychological connection between and ethics and religion; a moral code is one of the main facets of every religion in the world. Every major world religion teaches a morality of transcending the ego, a morality of charity, mercy, self-sacrifice, etc. Whether or not something is morally permissible or impermissible because religion says so is another argument.
Religion is invented by a culture to justify their own actions whether it be the Shinto, Buddhist, Norse, Islam, or Christianity: as ethics I would argue is based in human nature and society not religion.
We are social animals; we'v relied on others to survive from the very beginning we existed, we'v adapted feelings of empathy to the people close to us in times of distress, we learn from the social structure around us that assume rolls based in their material society that changed from carved bone tools to massive manufacturing plants altering the very basics of society structure and thus their ethics.
Religions isn't used necessarily for ethics, it's used for social control based in the ideology shared by the current social beliefs to enforce it's doctrine on others through justifying their actions through it. People will still pick and choose their beliefs according to how they were brought up and whether the world around them challenges those beliefs.
If you raised children without ever telling the child about a god, and provide reasonable conclusions as they get older on why committing certain actions like stealing and killing can be wrong, yet in some cases justified depending on preservation and social-being.
Overall, I believe current status of society and progress alter the ethics it lives upon which is the basic human nature guilt, empathy, sympathy.
Yes, religions set moral standards that may be unique.
But no, we also have a sense of morality quite naturally. Even the atheists know to be a good person, to harm no-one and stuff, so there's the common agreement on ethics.
Above this, religions may have different ethical code. However, since many religions have large parts made up by the ancient people, those religions' expectations to a certain extent demonstrate the morality and ethical standard of this group of people. In this case, Religion's rules are dependent on Ethics.
Human ethics came from the fact that humans are intelligent enough to be capable of feeling compassion and empathy and intelligent enough to determine what's right or wrong. Although religion enhances it through their doctrines, it doesn't necessarily mean that it is dependent on religion for I've known many Atheists and Agnostics that are way kinder than their religious counterpart.
Young children develop their own ethics when playing with each other. They socialize each other and keep themselves bounded with simplistic rules. As children develop, they are able to more complex rules and, through thousands of rules, this process continued to form religion. Religions' morals are based off of human interaction and teachings from those who found truth before us.