Remove protected posts from post loop

I'm trying to show a blog list with a custom loop in my site. I have created a shortcode that runs a query to pull all posts.
But it isn't checking against Membership rules. I want the loop to show a certain post only if the visiting member has access to it.
I read online that using a custom query doesn't check Memberships. I was hoping there was an argument I could pass or a filter in the foreach loop to check if the user has access. Any advice is appreciated.