After making sure there are no adwares/malwares, please do the following. Note, the reason I'm asking to do a scan is, some adwares/malwares prevent your Mac from applying or changing home page.
Click on Safari menu and select Quit Safari. Then In Finder, hold down Option key on keyboard, click on Go menu and select Library. From Library folder, open Preferences folder. Find and remove the files named com.apple.safari.plist and com.apple.safari.plist.lockfile (if you see it)
Then hold down Shift key and open Safari. Click on Safari menu and select Clear History or Website Data (or Reset Safari). Select All History and click Clear History.
(If you see Reset Safari instead, click it and Reset Safari)
This will clear all data of Safari like active logins, old cookies, temporary files etc (you will not lose any bookmarks or favorites).
Now click on Safari menu and select Preferences. Under General, change the home page to www.google.com or any others. Close Safari. Open it again and does it set the new page ?