How to list nodes that share one or more of the same entity references as the current node
You could get the blog posts related to projects refernced by the campaign displayed
through:

1- create a view  to get project id for projects have relation with that campaign.

2- create a new view listing blog posts that have relationships with projects taking project id as a contexctual filter.

3- create a .tpl file displaying the output of the view that gets projects from theme information

In that file embed blog posts view using views_embed_view() function giving the projects ids as a parameter for the view but you will need to 

Configure views to accept multiple parameters you should set this option: View → Advanced → Your Contextual Filter → More → Allow Multiple Values

you will loop through fields to extract and form the ids array and pass it as the code sample below

$array = array('32+50+32');
$view = views_get_view('myview');
$view-&gt;set_display("myblock");
$view-&gt;set_arguments($array);
$view-&gt;pre_execute();
$view-&gt;execute();
$content = $view-&gt;render();


By that you will be able to get blog posts from another separated view