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Two points.

I'm not sure what is wrong with the Customizer. It works in my browser. But after doing a bit of a Google search, I found a lot of people who have solved the problem of the Customizer not working specifically in Google Chrome, by adding "customizer.makerbot.com" to the Chrome browser's "cookie allow list". If you want to try this, you can find the Chrome cookie allow list in Chrome settings as follows.

Settings/Advanced/Privacy and security/Content settings/Cookies/Allow/ --> Add

After pressing the "Add" button, you can add "customizer.makerbot.com", to allow cookies for the Makerbot customizer.
I'd be keen to know if this solves the problem?

Another slightly easier way to download the source .scad file, if you want to load it directly in OpenSCAD, is to download it from the "Thing Files" tab. Just under the main profile picture of the model, you will see a row of tab buttons, "Thing Details", "Thing Files", "Apps", ..., "Remixes". Select "Thing Files", and you can just download the SCAD model directly from there, ready to be loaded into Open SCAD.
This is exactly the same as papavomsee's solution above, except that you don't need to copy and paste anything, as the file already exists.

This is in fact the best way to work with SCAD models, directly in OpenSCAD. As papavomsee pointed out, you have access to all the source code and can make more modifications that would normally not be possible in the Thingiverse Customizer. Plus, Open SCAD just works better than the Thingiverse Customizer. You can move and rotate the model more freely, which makes working with the model much more comfortable.

And, I like to think I am one of those modelers who's code is fairly neat, structured and well commented. ;)