Hi,

To be able to add a product to cart, three conditions need to be met product is active, can be sold is active and published to website. You can't add a product is not set as can be sold even if it's a rental product. 

Here you are the code of checking product:

def _is_add_to_cart_allowed(self):
    self.ensure_one()
    return self.user_has_groups('base.group_system') or (self.active and self.sale_ok and self.website_published)