With PixInsight closed drag the PixInsight folder from the applications folder to the Bin.
Hold down and keep depressed the keyboard Option key (on most Macs that is the middle key to the left of the spacebar, between the Control and Command keys), while the Option key is pressed mouse click on the desktop menu item GO and scroll down and click on the Library shortcut, the Library shortcut is only visible while the Option key is pressed.
Once in the Library release the Option key and then scroll down the folder list to the first PixInsight folder, open that folder to find two files, PixInsight.plist and PixInsightLicense, drag the PixInsightLicense file from that folder to your desktop then delete the entire PixInsight folder (mouse-right-click and select Move to Bin).
Scroll back up the Library folder and look for the Application Support folder, enter that folder and scroll down to find another PixInsight folder.
That folder contains two sub-folders, QTWebEngine and Default (the Default folder contain another four sub-folders and a few individual files), again, delete the entire PixInsight Folder.
Exit the Library folder and run the PixInsight Installer for version 1.8.8-9.
Launch PixInsight 1.8.8-9, depending on your hardware nothing much will happen for anything up to half a minute while PixInsight initialises and builds new folders in the Library, after that completes the first-launch registration entry page will appear, do not enter anything on this page, instead skip/cancel and exit.
Go back to the Library, (hold down the Option key while clicking on the GO desktop menu shortcut), scroll down the folder list to the PixInsight folder and open it, you will be in the correct folder if it contains just the file PixInsight.plist, drag the PixinsightLicense file that you placed on the desktop back into that folder.
Exit the Library folder and launch PixInsight, this should now launch with your old license file and not ask you again for your details, now test PixInsight to see if it still crashes on exit.