The first concern is the impact of shipping boxes directly to the homes of consumers. The transportation sector accounted for 27% of greenhouse gas emissions in the US in 2015. 40% of these GHG's come from commercial sources and freight trucks are one of the primary contributors. So whether you use a subscription service or shop at an actual grocery store, the closer you are to the origin of the food or products you are buying the better it means that your products don't require as much gas burning to get to you.
Packaging is also an issue, especially with mail cooking kits that you separate packaging for small portions of each ingredient. This can include plastic bags that can be recycled as well as bulky ice packs that keep food fresh.
All of this is to say that there are some surprising positive to subscription services for home products. A subscription service that sends its boxes directly to the consumer cuts out the middleman and eliminates an entire stage of transport as well as resources needed to stock in a storefront location. You may also be saving on gas used on your repeated shopping trips.
In summary, the environmental costs of subscriptions will depend on which services you use and how they operate. Do research on the options available to you. Go for services that are known for using minimal packaging and that recycles or has compostable choices. Blue Apron, accepts their packaging back for reuse and cycling. See if you can determine the location of the company's warehouse or shipping center. If the business is local to you there will be less negative impact shipping. Finally you need to do the math and consider if you're actually saving time and money by subscribing. If it's something that you need on a regular basis, it's much smarter and more environmentally responsible just to put it on your shopping list for the next time you're out.
If you decided that one of the subscription services is the right choice for you, take steps to mitigate environmental effects on your end. Make sure you diligently recycle. You may also want to try cooking delivery services every once in a while rather than subscribing. When you think you need something, plan ahead and make one monthly shipment. Buying in bulk is also better for the environment and it's also more convenient as you have on hand what you need when you need it. Isn't that really the goal in subscription services?