safari opens but then becomes unresponsive

You may  have adware/malware installed. Try downloading this program which was written by Thomas R, a long time poster. The program will search for malware/adware. The program will do the work for you which makes it easy. It may be necessary to run more than one scan. After running the scans, restart the computer.

Malwarebytes Anti-Malware for Mac      10.10 and later

Malwarebytes uninstall

I would uninstall Bitdefender. It tends to interfere with the computer's operation while providing minimal to no benefit unless you work with Windows files. Most long time posters recommend not using antivirus software or cleaning software such as CleanMyMac. They can adversely affect normal computer operation.

Bitdefender uninstall

Bitdefender uninstall (2)

Try setting up another admin user account in System Preferences/Users & Groups to see if the same problem continues. Please post back on whether or not this worked. Also try the Safe Mode. Please post back on whether or not this worked.

Isolating an issue by using another user account 

Safe Mode - About

If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor.  Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown. If the log won’t post, try posting it in Pastebin and provide a link in a reply. After pasting the report in a PasteBin page, go to the top of the page, and copy the address in the URL bar. Paste that in a new reply.        Pastebin

Etrecheck – System Information

I had the same issue with Safari only on one of the accounts on the iMac. It was getting unresponsive and most of the items in the top menu for Safari get grayed out!

The Reason was the same as you mentioned, Safari was asking if it should keep the Data from other browser (in my case Google Chrome) and that pop-up message got disappeared so fast that before seeing this post I didn't even notice it!

To solve it I took these steps:

> I changed the default browser to Safari and restarted but this alone did not solve the problem for me.

> Then I opened a Finder Window and selected "Application" from left side. it opens a Finder page with all the applications.

> By dragging that Finder window I aligned the window in a way that when I double click on Safari's icon in that window and when the Safari gets open I can catch that "Don't Keep" Button without moving the cursor.

> Clicking on the "Don't Keep" Button, did the trick and it's working now!

You might need to try it several time to get the right position for the cursor. Also every time if you miss it, you need to Force Quit Safari and try again.

There should be a better way to do that but until figuring that out, this might help others.

P.S. There is a screenshot from a part of that pop-up message.

Did you try Malwarebytes? It may not help, but try running/posting the Etrecheck report in your normal account. If the log won’t post, try posting it in Pastebin and provide a link in a reply. After pasting the report in a PasteBin page, go to the top of the page, and copy the address in the URL bar. Paste that in a new reply.        Pastebin

Try the Etrecheck report.

If you go to Safari/Bookmarks/Show Bookmarks, do the Firefox Bookmarks show in the Bookmarks Sidebar? If so, can you control - click on them and select Delete? Quit/reopen Safari and test.