Hi,
If you open the console of your browser when you are on a product page on your website you'll see these errors:
monosnap.com/file/AvrpkthpUCY7kp9b1fxBsMhhXvKO0W
The first one, which appears when the page is being loaded indicates that there is an issue with the javascript code in the header, near line 114.
It looks like this code is invalid if you look at the source code of the page :
monosnap.com/file/j4jBULYwenkqc63JpmW1XXKK6bwzTs
Because of that, the javascript code of HikaShop to handle the variants switching cannot be initialized by the browser. This leads to your problem.
So the problem is actually not in HikaShop.
You'll have to fix that javascript error (probably added by another extension or your template) and that will make the variant switching work again.
To identify which one it the culprit, you'll have to disable the plugins one by one (I would start with the plugins of the group system) and see if it changes anything.
also, you can switch to the default template of Joomla to see if it comes from the template.