First of all, know that this has NOTHING to do with stopping contacts from Gmail being added to my phone's contacts. I am trying to add a contact, but it keeps presenting me with a list of accounts to choose from to sync it with. I don't want to sync my contacts with any service. I just want to add them on my phone.
My phone is a Droid Maxx running Android 4.4.4. Do not assume that I am rooted.
If there's an option "local phone account" or something similar, then choose that instead of any Gmail account.
I can see this when I select "More Fields" in the "Add new contact" screen. Marshmallow, OnePlus One.
Install the MyLocalAccount app.
Go to "Settings → Accounts → Add account" and choose "MyLocalAccount".
Now in your normal, stock Android "Contacts" app, you can switch between accounts using the top-left hamburger menu "☰". Select the "MyLocalAccount" account from the top of it.
All contacts you will add will now land in the "MyLocalAccount" account, that is, on your phone only, without being synced to any server.
If you want to sync these local contacts to your computer, you can use the MyPhoneExplorer Windows application, which is the companion desktop software of the MyLocalAccount app. This will sync directly, without the involvement of any servers on the Internet.
Source: another answer here on Android Stack Exchange, and some own tests.
