A normal operating High Sierra installation would only display real Safari or Security updates in the Updates tab of your Mac App Store application. If something is popping up in Safari requesting your password, then you need to force quit Safari (option+command+esc) keys.
Download and run the free Malwarebytes for Mac, and see if it finds ad/malware installed. Let it remove them if it does.
Then, press and hold the shift key when launching Safari. Clear History : all history. In Safari Preferences : Advanced panel, [√] Show develop menu in menu bar, if not already configured. Press option+command+E to clear your browser cache. In the Safari Preferences : Extensions panel, disable all extensions. Quit Safari. Launch Safari normally. Have these requests for your password ceased on your screen?