There are many reasons people are uncomfortable with modern conceptual art:
Conceptual art is meant to be uncomfortable
The very objective of this form of art is to move you out of your comfort zone and give you new, yet unexplored avenues of thought. One must understand this idea, and appreciate the effect conceptual art makes on them. If a piece has a strong effect: it is good. If it has no effect or the effect is "eh": its fails.
Conceptual art is not classical art
Conceptual art has evolved form classical art where the objective was to capture nature and later human emotions, thus we tend to judge modern art by this same criteria, which is not correct. It's a different field. To be a great conceptual artists you don't need to be able to draw (although it does not hurt). You have to have novel ideas, and be able to conceive interesting ways to present them.
It's all about the idea
In classical art the actual piece of art (painting, sculpture, etc.) is what we evaluate. The back story makes the art more interesting, but it's not an integral part of the piece. In modern conceptual many times the art is just documentation of the idea. One must evaluate the whole story that's captured by this documentation, not just what's on canvas (or any other surface). One must appreciate the idea overall, not the aesthetic of the documentation itself.
When comparing classical art to conceptual art, the latter often fails, because our comparison is unfair. On one hand we are looking at selected pieces of classical art from art history: the top 0.01% of all classical art ever created. Most of classical art sucked too, there were plenty of uninspired artists out there, but they didn't survive the critics over the years. On the other hand, we're looking at all of modern art because it is still contemporary. Most of contemporary art is garbage too, but we don't yet have the benefit of hindsight. We should not judge conceptual art by this majority of poor quality work, but by the few good pieces, just like we judge impressionism by the few hundred best pieces created in their era.
It's self referencing
To fully appreciate and enjoy something you need to have a knowledge of it. If you want to appreciate a nice piece of ruby code, you need to know programming to a certain extent. If you want to appreciate a great fishing catch, you need to understand how hard it is to pull that off. You get the idea. In the subject of conceptual art prior understanding is even more important. You need to see lots of classical and modern art before you can fully appreciate modern art because it references itself a lot. It's very meta. And sometimes several layers deep. If you don't get a piece of modern art, the reason may be that you don't have the complicated background story that makes a particular piece of art clever.
It's not for everyone
You may understand what conceptual art is about and but you may still not like it because you don't like the very idea behind it. It's possible you are fundamentally a conservative person who doesn't like change, and you don't enjoy the feeling of your ideas about the world being disturbed. In this case, the best of conceptual art will be the worst thing you have ever seen in your life. An abomination, and a sign for of end of times.
Be open to the new, learn more and enjoy modern art on any level you can. Look for that feeling when your preconceived ideas as shaken a bit, or when a rush of unexpected new ideas are initiated in your brain by something you see or hear. Enjoy!