GET https://www.patreon.com/api/oauth2/v2/campaigns/${ID}/members?include=user&fields[user]=email
This response without email.
You would need to request the proper scope when authorizing users via your login process, then you can ask for the email with the resulting token.
What do you mean by “request the proper scope”?
Check out the scopes section in the api docs. They are permissions. If you dont get the user authorize with the right scope that a field requires, you cant get the field and entire call will fail even if you have the scopes for all the other fields.