Ok..
Might be corrupted Safari preferences
Open a Finder window. From the Finder menu bar click Go > Go to Folder
Type or copy paste the following:
~/Library/Preferences/com.apple.Safari.plist
Click Go then move the com.apple.Safari.plist file to the trash.
Quit then relaunch Safari then try setting your default search engine.
If that doesn't help, troubleshoot Safari extensions.
From the Safari menu bar click Safari > Preferences then select the Extensions tab. Turn that OFF, quit and relaunch Safari to test.
If that helped, turn one extension on then quit and relaunch Safari to test until you find the incompatible extension then click uninstall.
If it's not an extensions issue, try troubleshooting third party plug-ins.
Back to Safari > Preferences. This time select the Security tab. Deselect: Allow plug-ins. Quit and relaunch Safari to test.
If that made a difference, instructions for troubleshooting plugins here.