Should I add "nofollow" to all my outbound links?

In the name of SEO we've received requests to add a "nofollow" attribute to all outbound links on a site. Unfortunately there is no definitive conclusion regarding whether this is a good or bad idea. 

According to Google, nofollow links don't get crawled by their systems, and they recommend using the nofollow tag on paid (affiliate) links. We recommend you use nofollow only for affiliate links or for links to spammy sites. 

What is nofollow?

Nofollow/dofollow instructs the search engine bots whether or not to follow and index the links. You can say that a dofollow link is a tiny endorsement because it passes "link juice" to the page that you are linking to. Nofollow links give no juice.
If you want to make a single link nofollow or dofollow, add it to the link's rel attribute as in the following example. You can edit this if you view your post in Text mode in the WP Editor window.
<a href=" http://wordpress.org/" rel="nofollow">wordpress!</a>
By default WordPress designates all user-submitted URLs as nofollow (e.g. in comments), but there is no default for links in your own content. You need to add the rel attribute yourself. If you want to set it up so that all external links are automatically set as nofollow, or you want to override the default and make comment links dofollow, there are a variety of plugins that do either/both of these things. Send an email to support@performancefoundry.com and we can recommend one to you.

What about NoOpener? Is that similar to Nofollow?

NoOpener and NoReferrer are completely different to Nofollow. They affect how the browser deals with the link, and WordPress has made them default for links to address a security vulnerability. You can read more about them in this Knowledge Base article:  Why do my links have "noopener noreferrer" on them?
There is no SEO impact from using NoOpener and NoReferrer tags, so you needn't worry that it will diminish traffic to your site.