One thing I've been thinking about is if I didn't believe in God, what religious rituals would I retain? Or in other words, what does science have to say about religious rituals or values?
Spend time with family, get closer to family. This one seems pretty obvious. A common way to spend time with your immediate family is through family dinners, which are correlated with a lot of positive things, and have a pretty good effect on lessening depressive symptoms and helping children feel they have a stable environment. One problem with family dinner research is that it is hard to separate families who eat together from families who are middle- and upper-income brackets. This article explores the limitations of such research. There's also the BYU study about how daughters who played videogames with their parents exhibited more pro-social behavior and felt closer to their families. I like the Mormon tradition of having a night set aside to spend with families (Monday night is "family home evening"), and I think it logically follows that if you spend more time with your family, they will know each other better and feel closer to one another (whether or not your family members like being close to one another is up for debate though).
Gratitude. Being thankful for things in your life and for the things other people do for you is associated with feeling happy and optimistic and such. There's a time and place for cynicism, but personally I don't struggle with being a realist and I could use a dose of optimism some days. Daily prayers encourage us to be grateful, but if you don't pray, you could have some of the benefits of prayer by taking a little time each day to think about what you're grateful for.
Goal-setting. This isn't a religious ritual per se, but when I pray for something I feel like it's a goal I've set and I start to think of ways I can help make it happen. Of course, sometimes I pray for things I have no control over, but I think that the act of praying for something can make you more receptive to having ideas about how to help that desire.
Prayer. I'm not sure if you have to believe in God in order to pray. There are benefits to praying, like if you pray for your spouse or friend you are more likely to forgive them, and some people experience less pain. Maybe part of the relaxing effect of prayer is having faith that God is taking care of you, and that praying will help you in your life somehow. When I pray for someone, it motivates me to see things through their eyes and have more compassion towards them. I'm not sure what the secular equivalent to prayer would be--maybe meditation?
Knowing your family narrative helps adolescents have a fallback identity. In my religion family history work is part of our missionary work, since we believe that we can perform saving rituals (like baptism) on behalf of the deceased. Most people don't know very many dead people, so you start with your own family members.
Those are a few I've thought about. I think there's probably a benefit of knowing other people who live near you (like the people you meet at church) and having adults other than family members interact with your children.
A few weeks ago I got sick of everything in my Facebook feed. Everything was vanity. First I was only going to hide articles from other sites, because I decided I wanted Facebook for people news. Then I realized I was getting a lot of updates from people I didn't care about that much. So I went through all my friends and put them in groups, and unfriended a bunch of people I barely remembered. I felt sentimental about people I had met as a child and teenager though, so I kept most of my friends from my growing-up years, even though I have little in common with them (but I put them in a separate group).
But it wasn't enough! I was still getting stupid stuff in my news feed. So I unfollowed every last person in my news feed. Sometimes it was hard to unfollow someone, but I kept reminding myself that if I really wanted to know what someone was posting, I could always visit their individual page. As I started unfollowing people, friends I didn't even know were active on Facebook started popping up in my news feed (like my aunt!). I unfollowed everyone and soon I realized that my news feed could have an end. For good measure I unfollowed everything I had liked, and I unliked almost everything. It was such a relief.
Maybe completely breaking with Facebook would be good for me, but I like hearing little updates from my friends and family in our post-blogging social media world. Dividing my Facebook friends into groups was very helpful, because now I can choose who I want to hear from. If I only want to spend a few minutes on Facebook, I click the "family" friend group. If I'm bored I can explore the other groups, but I have to make a conscious decision to continue.
This method of sorting one's feeds has its pros and cons. I don't think anything is filtered this way, so I see everything any one person in the group posts, likes, or makes friends with. In some ways I like it better, because I can be sure that I'm not just in an echo chamber where I see what I like, and I can know that I'm not just seeing the most controversial posts. But the ordering isn't based on when the post was made; if someone comments on a post it comes back to the top again. Redundancy of posts was one of the things I hated in my original feed, and I still have no way to fix this problem (although for my friends with blogs, I don't really read your feeds much anymore, I just read your blogs). I also wish that more of my Facebook friends would stop sharing pithy quotes and photos and start telling me more about how their day was or what they are thinking about.
But on the other hand, I've enjoyed reading articles my friends have posted in the past and using them as a starting point for discussion. The majority of the posts I read on Facebook are made by 3-4 people (if you post or share to Facebook more than once a day, you know who you are), and I don't feel like I am any closer to those people than the people who don't post much, but I might have more topics ready for conversation since you are on my mind more.
I don't think I'm done with Facebook experiments--some time I want to try commenting on everything in my feed, just because. And maybe there's a browser extension that can hide all the stupid "x is friends with y and likes z" I have in my feeds now.