HTML, CSS and accessibility standards
There is nothing in the Shop Banana product that prevents adherence to industry standards for HTML, CSS and accessibility.
This is as much as any ecommerce product can say, because it is always possible for your own customisations to break these standards.
Javascript
A Shop Banana website will work on browsers that have javascript disabled. Some of the more advanced features use javascript, but javascript is only used to enhance functionality. It is always possible for a customer to browse, search and purchase products on a browser that has javascript disabled.
Again, this comes with the proviso that your own customisations don't prevent the site working properly if javascript is disabled.