What you are asking for is arbitrary actions related to an issue without authenticating, its a pretty niche feature that quite rightly is not possible by default.
The only solution I know of is the one we wrote( as part of Enterprise Mail Handler (JEMH) for Jira (disclaim: its our product!), where we allow custom tokenized urls to be placed in HTML notifications that JEMH generates (even with nice css AUI buttons for Accept / Reject), enabling a Set of issue manipulating Directives to be used to update an issue.
See the Use Directive Sets page on our wiki, specifically the "Use in workflow" section.
The Fundamentals are that ion the email template, you nominate a context user for the related operation, possibly the recipient, and refer to a predefined 'group' of Directives (all standard issue fields), every time a related email is sent, a new instance of clickable link tokens is generated that can be used in the email. When one link is used, all other in that set are removed, so its a one time, non-reversible, unhackable solution.
I should also say, due to the nature of JSD, you can either have JSD notifications in a project or JEMH, not both.
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