Functionally, it's not possible as of v8.0 because all the fields that have an effect on displaying the variant on the website impact the whole product template, not only the variant. That is the case for the Publish button and the Can Be Sold checkbox.

The only way to do this is technically, by coding a QWeb condition to hide the variant from the page.

Hello Emipro Technologies,

Technically when you unpublish the product varient, it will unpublish the whole product from the store, because the product varient inherits the product template.
and if you do change in product varient, it will be directly affect on the product template. Unpublish button do the same. 
So solution will be to inactive the product. 
if you want product in the report, you can customize your report accordingly.

Hope this Helps.

Hi,

is there any update on this topics by any chance?

Is it now possible in odoo 14, 15, 16? 

Thanks.