I've created a welcome series on-boarding Journey. I want to give new users the ability to opt out of this journey. I want to use Publication Lists to do this.
How do I associate a Publication List to a Journey?
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A publication list wouldn't be associated to a Journey itself, it would be associated to each individual email.
So in the email configuration screen within your Journey, on tab 2 - "Email Send Configuration" - you would select which Publication List is associated to that email, meaning if they are unsubscribed it won't be sent to them. Just make sure to apply the same publication list to each email in the Welcome Journey.
Hope that helps!
+1 for Atilla's answer. See also this: Email Subscriber Lists and Journey Builder https://help.salesforce.com/articleView?id=000213370&type=1
Knowledge Article Number 000213370 Description
Since the Contacts framework used by Journey Builder only supports records stored in Data Extensions, Journey Builder does not support the use of lists created in the Salesforce Marketing Cloud Email application.
Workaround In order to move subscribers from a List to a Data Extension, a Query Activity can be created to query all subscribers present on a specific list, and output to a Data Extension that's compatible with Contacts and Journey Builder. The Query Activity may be used as a step in Automation Studio in order to automate this process on an ongoing basis. The data extension could then be linked to either a new or existing attribute group in Contact Builder.
By the way: You can also accomplish this via storing the recent information in a Data Extension for your subscribers, check this at the beginning of the Journey & end Journey if applicable.
As an alternative create a Journey-specific Data Extension from your Publication List as an Entry Source. Update the DE via Automation Studio.