Should a retail web-site always return the same items for identical searches made by different users?

We supply a large number of products for purchase through our web-site. There is a new initiative to apply a third-party AI product to hijack searches to return products based on both the search term and predictions from browsing history and other people's search history with successfully processed sales. If I now search for a keyword, I will get a different set of products returned than if someone else searches for the same thing. If I pass an URL of my search to a friend to compare the products, we will have different lists, so cannot discuss. The list, I find, changes day-to-day, on my own machine due to the AI's suggestions.

Is this a design "no-no"?

Should the AI be solely used for recommendations and not for the core search results?

Is there any guideline to cite that makes suggestions on this?

I have also put this on: Software Recommendations