Hello, It is completely possible, depend on your current product management software the method for gathering data for making unique groups with their allergic or other attributes can be vary. You can also add an online panel or system to increase the speed of this process; for example online surveys or extra discounts for filling some subscription forms with personal data

If you like to speak more about it, we can have a call on defining a system or even setting up an online branch for your current business.

If you're on a tight budget, you could do a simple combination of Wordpress (WooCommerce/Stripe) and MailChimp to gather and store customer information and preferences, process customer communications and shipping notifications, and automate deliveries. It'd be a bit manual for setup, but I'm convinced you could move the data between the systems at low-cost and enable accurate drop shipping, depending on your products. Of course, you'd rely on customer input to store preferences (allergies, tastes, etc.), and this input could be gathered a number of ways, perhaps through surveys or through a customer preferences profile required during the buying process. Once the customer lists are organized and the systems are connected, you could automate the vast majority of it (at low cost). A little bit of hustle to put together, but way cheaper than the fees associated with many CRM systems.

It makes sense that info would have been gathered when the order was placed, so it should appear with each order. If the problem is that your products are too generic to the point where it confuses who you have fulfilling the order, you can create new products in your shopping cart that are more verbose.