Question
Can morality exist without religion?
Yes. Religion can shape moral systems, but morality can also be reasoned from suffering, wellbeing, fairness, responsibility, consequences and social life.
Answer
Many religious traditions teach moral rules, and for many people religion is their first language of morality. That does not mean morality depends entirely on religion.
Human beings can reason about harm, fairness, trust, cruelty, responsibility, freedom, care and consequences without first appealing to divine command.
There is also a problem with claiming that morality depends only on religion: religions disagree. If different traditions give different moral commands, then reason is still needed to compare them.
This does not prove that religious morality is useless. It means moral claims, including religious moral claims, should be examined by reason, evidence and consequences.
Evidence
People from many different religions and from no religion at all can recognise suffering, fairness, care, trust and harm.
Moral disagreement among religions means reason is still required to judge between competing moral claims.
Alternative views
Some traditions argue that morality requires divine command. A reasoned response is that divine command claims themselves still require examination, especially when different religions report different commands.