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This question has come up a lot and there are several different answers that are all correct in various situations. Let's take a few minutes and explore some of these.
First off - I generally do not recommend excluding anyone from the opportunity to record an NPS opinion. In almost all cases the user will simply complete the survey or simply close it. The trick is having an NPS platform that allows you to perform powerful filtering. Maybe you can explode a certain group from your analysis or perform an analysis on a subset of groups. I have almost never seen problems arise from asking the entire customer base.
Let's look at an example. Let's assume you have a customer that is having a charge dispute with your company. Providing them with a feedback survey - after the dispute has been resolved - is a great opportunity for you to ensure that the resolution was satisfactory. In many cases the customer may become more loyal after their customer service experience. If they had a bad customer service experience then maybe work needs to be done in that area.
I also don't advise excluding key partners, employees, beta testers, etc… The primary reason is that these are generally the folks that are dog-fooding or seeding the initial activity in your product or launches. Put another way, these are often some of the first users to come in contact with your product or new features. Their feedback can be a valuable early warning system on potential issues. Before you launch a feature you should release an internal NPS survey in your company asking employees to test the feature and provide their recommendation on it. This provides very powerful data.
Customers who have opted out of email communications is another group that comes up often. While it is true that you cannot send an e-mail to these users for their feedback, there is nothing that prevents you from providing an NPS survey to these users when they visit your site. In fact if your NPS analysis tools are smart enough they may be able to segregate these users into a side group and allow you to get data as to why these users don't appreciate the e-mails.
The best way to wrap this up is to say that there are very few circumstances in which you should not provide the opportunity for customers to fill out the NPS survey. The key then is during the analysis phase when the NPS score is calculated. You can calculate multiple NPS scores for various customer groups and obtain richer information into the sentiments of your company.