What outcome are you after?
In the example screenshot you have above, you're making a connection over HTTPS, but for whatever reason your certificate isn't trusted. Out of the box, this is because ArcGIS Server uses a self-signed certificate for HTTPS, and by definition self-signed certs aren't trusted. By default, ArcGIS Server supports both HTTP and HTTPS connections. Note that while you're getting a 'Not Secure' message in your browser, switching to HTTP would actually be LESS secure because sensitive information is being sent over plain text. Any endpoint where sensitive information (like usernames and passwords) are passed should be accessed over HTTPS.
With that said, unless the GIS Server has been configured to require HTTPS connections, you can reach the server over plain text at http://server.domain.com:6080/arcgis/rest.
The BEST guidance that can be provided would be to obtain a certificate signed by a well known certificate authority, install it on your web server, and configure the web adaptor. That way you'll have a valid, trusted certificate that won't cause your browser to show messages like the one you're describing and at the same time you'll improve your security posture.