Hi..
Since this is happening on Safari on both Macs, restart your internet modem and Wi-Fi router if you use one to see if that makes a difference.
If not, a Safe Mode boot deletes system caches that may.
Top left corner of your screen click the Apple > Shut Down.
After your Mac shuts down, wait 10 seconds, then press the power button.
Immediately after you hear the startup tone, hold down the Shift key. You should press the Shift key as soon as possible after you hear the startup tone, but not before.
Release the Shift key when you see the gray Apple logo and progress indicator.
Once you are in Safe Mode, go back to the Apple menu. From the drop down menu click: Restart
Then try Safari on both Macs.
If that doesn't help, you may have installed the same third party Safari extension or plug-in on both Macs that's causing a conflict. It's easy to troubleshoot.
From the Safari menu bar click Safari > Preferences then select the Extensions tab. Uninstall one extension then quit and relaunch Safari to test.
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.
About Safe Mode