Hi @str  - welcome to the community!

As I understand it, the Back In Stock opt-in behaves more like a Metric (Event) rather than a List subscription and used to trigger your Back In Stock Flow when an item becomes available. In other words, it doesn’t technically go into a List (even though you can build a Segment of people who have requested a Back in Stock). 

My experience is this isn’t technically a marketing consent opt-in, so Double Opt-in isn’t required.  Not to mention, people can opt into multiple Back In Stock - either for the same product (if it goes out of stock again) or different products/variants at the same time.

If you intend people to also Opt-in to general marketing consent, you can add additional parameters in your Back In Stock modal and state it more explicitly so the subscriber knows that they are opting into marketing (and not just Back in Stock notifications). 

Often, I’ve seen people put a checkbox option so people have can also conveniently opt-in into general marketing like the example in the documentation:
 

The documentation below explains how to set this up by modifying the code snippet, but copying here for convenience. 

The "klaviyo.init" section will look like this:

klaviyo.init({
        account: 'PUBLIC_API_KEY',
        list: 'YOUR_LIST_ID',
        platform: 'shopify'
});

You would add the List ID of the List you want the Subscriber to be added to, in your case the Newsletter List that already has the Double Opt-in enabled. 

I think in this way you get the best of both words:

• People have the option to opt-in to your marketing messages, and know to expect this. They will get the Double Opt-In confirmation that you have already setup. That way, when they do get your Campaign emails, they aren’t surprised by it and either ignore it or worse, mark it as Spam.
• People who just want Back in Stock notification will automatically get those emails without having to confirm the Double Opt-in email confirmation step.  

Hope this helps!