If your store is using a password page on its storefront ( https://help.shopify.com/en/manual/using-themes/password-page), then Cross Sell is restricted on our ability to search your shop's product. Cross Sell's filter ability when storefront password is activated is limited to 2500 products.
If your store has more than 2500+ items and you wish to assign cross sells, you'll have 3 options:
1) De-activate your storefront password while assigning cross sells.
2) Use an app like Locksmith to password protect your store (while it's in development) instead of Shopify's password page
3) Request a Bulk Upload and send it to us for bulk uploading.