I'm looking to export only wp_posts where post_type = post.
Is that possible?
In your WordPress Dashboard, if you go to
Tools > Export, you can select your custom post type and export only posts in that post type.
It gives you the option between All Content, Posts, Pages, and your custom post types following those three options.
As for SQL, well are you looking to export the data from something like phpMyAdmin? You could use this:
SELECT * FROM `wp_posts` WHERE `post_type` = "post type name here"
Hope this helps.
Also, as kaiser pointed out in a comment, you may need to deactivate all plugins and switch to the default theme.