I'll start with maybe I just don't know enough about open source. I do understand that the code is available and people can see it, make suggestions or adjustments, or essentially make their own thing using some or all of the code. I'm all for sharing things as necessary and learning from others when possible. With this though, I personally am on the side of: I trust ljdawson to do what's best for this app. I am on the sync train because of him the incredible app he made, and how he leads and interacts with the sync community.
I've been using Sync for about 7 years and I've always thought Ljdawson is very active with the Sync community and (from my experience) has been pretty receptive to feedback on his app. When the material you version of Sync came out, people didn't like it so he made it so you can choose between the material you look or the old look. There are tons of customization options. I feel very informed with each update as well as what his next plans are. There are paid features that both support him as a dev and the longevity of the app. He puts a lot of time and care into creating the product we get to use and for me that is more important than being able to access the source code.
I understand the worry for sure. My gut says that stems from the current situation at reddit, but I personally don't think the answer is sync going to open source. If something crazy happens with sync, there are (currently) other options.
If your phone is Android... then the phone's operating system is "open source" ( for reference ). Also, the kernel of Android is Linux, which is, itself, an Open Source project.
Now, those are just the core systems that run an Android phone. Obviously not every app on the phone is Open Source. Most likely, not even the majority of apps are open source. That said, if you look into it, you'd probably be surprised to find far more Open Source apps on your phone than you think there are.