I'm working on a site that has got some heavy relationships (post-type related, ha!). Is it possible to do something in order for those to not be that resource intensive?
Can you please give more details about your question? Do you mean cache the query when setting up the connection in the admin area or show the connection post in the frontend?
I mean when the connection is shown in the frontend. Monitoring the server usage, when having the relationships queried, we get some spikes/high consumption. If we disable them, the high usage is mostly gone.
The relationship injects the relationship parameter to the WP Query of WordPress and its data from a custom table so I think it won't affect the performance significantly. You can try using a caching plugin to cache the query like WP Rocket or Redis Object Cache to prevent high consumption on your site.