I had the same problem today (just after updating my phone) and eventually found a way to uninstall Google Play Services updates, thanks to the thread in Google Play Help Forum:

I was able to fix the issue today, by uninstalling the Google Play Services updates. Could only do that after making sure 'Find My Phone' was no longer a device administrator. Steps I followed:

1. Go to Settings -> Lock screen and security -> Other security settings -> Device Administrators
2. Uncheck 'Find My Device'
3. Go to Settings -> Apps -> Google Play Services
4. Tap the vertical ellipsis (3 vertical dots) at the top right -> Uninstall updates
5. Go to Settings -> Apps -> Google Play
6. Tap the vertical ellipsis (3 vertical dots) at the top right -> Uninstall updates
7. Restart phone. At this point the message "Google Play services keeps stopping" was gone.
8. Open one of the Google apps (in my case Google Maps)
9. It complains that "Google Play services" is outdated, click the popup to update it again. Problem solved. Really happy to have my phone back ;)

It worked for me (no more error messages, and now I can use again apps such as Google Play Store, Google Maps, etc)

Solution 1 – Update Google Play Services to the latest version. You can download from here. You may be getting an error because you have a very outdated version or the one you have is having a conflict/bug with the current Android version in your phone.

(source: teamandroid.com)

Solution 2 – Clear the Google Play Services cache. The Google Play Services app in your phone acts like a framework for all the Google and Google Play apps installed in your phone. You can try cleaning up its cache and see if that would fix the issue. This worked with one of our team members! Read these quick and easy steps:

Go to Settings > Apps.
Scroll to All apps and then scroll down to “Google Play Services” app.
Open the app details and tap on the “Force stop” (see "Force stop is disabled" below) button.
Then, tap on the “Clear cache” button.

Solution 3 - Uninstall the updates of "Google Play Services".

As in solution 2, go to Settings > Apps.
Scroll to All apps and then scroll down to the “Google Play Services” app.
Open the app details and:

1. Tap on the “Force stop” (see "Force stop is disabled" below) button
2. Tap on the "Disable" button
3. Tap on the three dots at the top right and select: "Uninstall updates"
4. Once the uninstallation is completed, tap on the "Enable" button

Solution 4 – Clear the Google Services Framework cache. The Google Services Framework system app on your Android device stores information and helps your phone sync with Google servers — and keeps your Google Play Services up and running. This could be one of the reasons why you are not able to connect to Google servers using the app and keep getting the error message. Read these quick and easy steps:

Go to Settings > Apps.
Scroll to All apps and then scroll down to “Google Services Framework” app.
Open the app details and tap on the “Force stop” button.
Then, tap on the “Clear cache” button.

Solution 5 – Check your Internet connection. Maybe your WiFi network is blocking any of the IP addresses that Google uses. You can also try switching the WiFi on or off on your phone — same with mobile data.

Solution 6 – This goes without saying, but maybe a simple reboot of your Android phone/tablet could fix the problem.

Solution 7 – I hate to say this, but in the end, you might just want to install a custom ROM that is stable with no bugs.

Force stop is disabled If either the "Disable" or the "Force Stop" buttons are disabled then:

1. Go to Settings → Device admin apps
2. Deactivate the following apps if they are listed:
   • Find My Device
   • Google Play

^{(example on Android 8.0.0, Samsung Experience 9.0.0)}

Note: Please, keep in mind that you may have to experiment with what apps you deactivate.

Your device admin apps list may differ. For example, you may have more or entirely different apps.

I have found that disabling the above two apps was enough for me to disable and force stop "Google Play services".