The software is not open-source but both Mapillary and OpenStreetCam have very permissive licenses. I contribute to and use both services to improve OpenStreetMap.
OpenStreetCam itself isn’t quite closed-source: it is on Github. But the app was built on top of Facebook tools, which many people will not want on their phones. See the notorious outstanding Github issue [0]. At least OSC’s hard dependency on Google Play Services appears to have been removed, though – last time I looked into installing Mapillary, it still would not run on a bare Android like LineageOS.
[0] https://github.com/openstreetcam/android/issues/8