Yes, I believe you can have morals without religion.
Mainstream religions are essentially collections of social norms plugged into a framework of suggested supernatural powers. As we evolved from solitary bands of roving hunter/gatherers to a more settled agrarian society, we needed rules to prevent chaos. The latter half of the 10 Commandments are an excellent set of rules that would allow people to love together in harmony. Respect your parents, don't murder, doink your neighbor's spouse, steal, lie, or obsess over what someone else has.
What better way to lend weight to these ideas than to add an element of supernatural risk - failure to comply will lead to a post-mortem eternity of suffering. Organized religion is just the vestigial part of the storytelling that passed from generation to generation.
So, yes you can be moral and spiritual without organized religion.
This is the Pub. Leave common sense at the door.