Austin from WP Engine here.
Ajay is 100% correct about not being able to run plugins that use FULLTEXT on WP Engine. Here’s the post we wrote with all the details: https://wpengine.com/2012/06/fulltext-update/
TL;DR is that FULLTEXT is more or less fine if you don’t get much traffic, but our infrastructure is set up to scale aggressively, which means we cache everything possible and avoid hitting Apache everywhere possible because that slows things down so much. Querying FULLTEXT more or less negates this, and causes a lot of performance issues for your sites. At best, it slows response times down. At worst, it craters the entire server.
In the post, we recommend taking a look at nrelate and Wordnik for similar functionality.
Also, so you don’t have to take my word for any of this, check out the blog post I googled from Chris Lema about Related Posts plugins: https://chrislema.com/related-post-plugins-handcuffed/. That should provide a credible second opinion here.