I think I have sort of worked out a solution. It displays correctly in the Views preview but not on the node itself. Maybe this will help though.

View settings: 

Create a Block. Configure Block to display on content of type Post. Configure settings of View:

Fields


Content: Title


Filter criteria


Content: Published (Yes)
Content: Type (= Links)


Contextual filters


(field_tags) Content: Title

Using relationship: Term



Relationships


Content: Taxonomy terms on node (term) 
Taxonomy term: Content using Tags

Using relationship: term



In my preview, when I enter the title of a Post as the contextual filter, I get a list of all the links tagged with the same tags as the Post. For some reason, when I view the actual Post it doesn't work but that might just be a caching issue or something on my end?

Views Taxonomy Term Argument With Multiple Terms
Is there a way to close all the open file descriptors, without having an explicit list of them beforehand?
