Here is a crazy fact... Google Maps doesn't require Play Services to be installed. About once a week it will popup a message about no services installed, but it still functions (other than logging in).
In my experience this goes for most - for me actually 'all' but I don't tend to use much from the Play store - apps which insist on having Google Play services installed. They blatantly tell you to 'Enable Google Play services' because (e.g.) BankID won't work unless you enable Google Play services. Just click outside of the dialogue to make it disappear and use (e.g.) BankID as normal, it just works as it should.