To protect their business reputation, most companies invest a lot of money to make sure you can log in securely and use your account. What you need to pay attention to is whether your network is secure and visits the correct website address. Here’s the information that has been manually reviewed about login skype with gmail :
Skype
https://secure.skype.com/portal/overview
Cannot access Skype using my gmail account – Microsoft …
https://answers.microsoft.com/en-us/skype/forum/…
May 17, 2018 · Microsoft no longer supports Gmail or Facebook accounts for signing into Skype. Your best option is to setup a new Microsoft Account if you don’t have one already: https://support.skype.com/en/faq/FA12125/how-do… Best, Andre. Windows Insider MVP. MVP-Windows and Devices for IT.
Sign in – Skype
https://clientlogin.cdn.skype.com/cdn/6.0.1/release/index.html
Skype or Microsoft account. Sign in with Skype or Microsoft account. We’re having issues signing you in. Please try restarting Skype. (c4)
How do I sign in to Skype? | Skype Support
https://support.skype.com/en/faq/FA12125
Skype and click or tap Skype name, email or phone. Enter your Skype name, email or phone and select Sign in. Enter your password and select the arrow to continue. You’re now signed in to Skype. Note: Once you’ve signed in, Skype will remember your sign in information when you close Skype or sign out and choose to remember your account settings. If you …