There are some important things you can do without resorting to alternative OSes.
To start with, it’s not mandatory to have a Google account even when using the stock Android OS, the OS itself will work just fine without one.
The respective setup step in the initial Android setup can be skipped, or an account already added can be removed in the Android settings later.
Certain Apps might require a Google account, though, Apps by Google themselves foremost.
But there’s a conscious choice to make of which Apps one wants to use for which purpose, mostly there are alternatives available to choose from.
Then there are a lot of default settings phoning home, but which can be altered. It’s worth to take some time to sift through the whole settings tree. It’s quite informative anyway.