After unchecking "discourage search engines" the homepage disappears

What do you mean with disappears? Blank home page or you can still see the header and the footer (for example)?

Thanks for answering.
Header and footer still there, between there’s a narrow horizontal strip. All the other pages are ok.

Ok, so take a look at Settings -> Reading
Front Page displays.. what does it stay?

Nothing selected

And you want this because?
I mean do you want to display something on it?

Of course, the built-in slider page

There’s no built-in slider page. There’s a demo slider, but no page .. so ..
If you try to show your latest posts from Settings -> Readings, does it work?

Sorry, no not the built-in but the created slider. Busy now, I’ll check it out later this evening. Thanks.
BTW Yoast installed, maybe I’d deactivate that one.

In Readings, when I select “Your latest posts”, it works!. However there are no posts created on this site, and it is not intended to do so. So I guess it is ok like this, although it seems like kinda workaround.

So basically the problem is that when you select to don’t show anything on the front (in Appearance -> Customize -> Content:… -> Front Page) the slider doesn’t show up..?
Cannot replicate it :/
Could this be due to a conflicting plugin?

That is correct.
Tried to deactivate the Yoast, no difference.
Active plugins are: InPost Gallery, Very Simple Contact Form, WordPress SEO (Yoast) and WR PageBuilder.