MongoDB: All commands spit out "not authorized on admin to execute command"
Let's try this:

Connect to your DO droplet.

In your /etc/mongod.conf, comment out 'security' and restore bindIp to value 127.0.0.1

Restart your mongod instance.

Connect to mongo (at this point without security).

Create you admin user in mongo with something like this:

use admin
db.createUser(
  {
    user: "myUserAdmin",
    pwd: "abc123",
    roles: [ { role: "userAdminAnyDatabase", db: "admin" } ]
  }
)


Make sure the user was successfully created.

Go back to your /etc/mongod.conf. Set your bindIp value as: 127.0.0.1,YOUR_DO_DROPLET_IP (no spaces between). 

Uncomment 'security', keep 'authentication' commented out, add below it 'authorization: enabled'

Restart your server's mongod instance.

Connect to mongod remotely by using: 

mongo YOUR_DO_DROPLET_IP -u myUserAdmin -p --authenticationDatabase admin


References: 
MongoDB Authentication
Enabling MongoDB Authentication