First of all you need to know that you are not the only shopper getting those emails. Each notification is going out to many other shoppers in your area. It is not necessary to respond to the emails and say that you are not interested. You only need to take action if you want the assignment.
Even if you respond and say that you are interested in doing the shop you are not guaranteed the assignment. The email went out to hundreds of other shoppers in your area, and one of them may get the shop.
The sheer volume of the number of assignments and possible shoppers means that it is not likely anyone will notice whether a particular shopper is applying for shops or not, so whether or not you accept shops will not affect your eligibility for future assignments.
What about when they call?
When a scheduler calls with an assignment, it usually means that they are up against the wall and need the shop done ASAP. Often that is because another shopper flaked and didn’t do the shop they accepted, or it may just be that they have a hard time assigning certain locations.
I generally try to help out in this situation because I know that if they are calling the shop is probably urgent. However, there are many times when I have to, or choose to, say no. I have never noticed any difference in the offers coming from these companies after I say no to a request.
When a scheduler calls with an emergency shop request, you may want to ask for a bonus. Chances are that completing a last-minute shop will force you to rearrange your schedule and if it is a hard-to-fill shop it may mean driving some distance. Asking for a bonus is certainly reasonable. Asking politely for extra pay in special circumstances will not mean that you will not be offered future shops.
So, the short answer to the question of whether not accepting shops will get you blacklisted is no, it will not affect your ability to get other shops. However, accepting shops, especially in a scheduling “emergency” may lead to more shops from grateful schedulers. At the very least, you may be able to negotiate a nice bonus for helping a scheduler out of a jam.