The attachments in Jira belong to the issues, and hence are subject to the same security and permissions.
To make them available to people outside your organisation, you'll need to expose the issue to those people - this can be done by making the issues available to anyone. But it really does mean anyone.
You've got other options, but they all need a bit of work. I've seen attachments made available (read only) on a file share with a script that allows the share system to serve up the file without having to dig through it. You can use plugins to attach and send attachments to non-Jira users via email, although that might not be as good as a file store as theyre a snapshot and could become obsolete. You could mirror some/all of the attachments into another system - I'm thinking of a Confluence macro I saw that would put some fields from a Jira issue into a page, and it would include the attachment in-line.
So, you've got options, but you need to do some thinking about what you publish to whom, and then work on how you'd ideally like to get the attachments to your external users.
Bear in mind that all of these are potential security leaks - you're sending stuff to people and bypassing the access controls in Jira. Not a problem for most people, but something you need to consider before allowing it (Even if the answer is "meh, it's fine for anyone to see this stuff", you need to be able to demonstrate that you've considered it)
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