I'm working with NRF5 SDK. Most of its source is available (no idea if it's free software or not, but sources are there). The most glaring exception is softdevice - that's BLE implementation, it's huge binary blob, taking control over most CPU.
Their newer SDK based on Zephyr RTOS, I didn't work with it, but I think it's mostly open source as well.
You can use NimBLE on quite a few of these chips.