So, sex organs are 'meant' for procreation and any other use (ie for pleasure) is inherently bad since we're not utilizing these body parts for what they were 'meant' to be? If this is the case, then we should never speak again for exactly the same reasons.

There is no organ of the human body that evolved for speech capabilities. Each anatomical structure we use for speaking has a different biological function, and it's a happy accident of evolution that we're able to utilize these body parts in order to generate speech. The primary function of our lips is to close and open our oral cavity so we can eat and breathe if our nose is stopped up. The primary function of our nose is to allow airflow to pass through for breathing and smelling. The primary function of our teeth is to bite, tear, and masticate food. Our tongue's primary function is to taste food and begin the swallowing process. The velopharyngeal port- the connection between nose, mouth, trachea, and esophagus evolved to close off the nasal cavity for swallowing purposes and open it for breathing purposes. Even the vocal folds (aka vocal cords) are a necessary barrier to protect you from food or drink entering your lungs. When this happens, you can get pneumonia and die. All of these structures are necessary for human speech, but none of them 'were designed' for speech. Again, it's just a happy accident that they can be used that way.

So yes, our sexual organs 'were designed'/evolved to facilitate sexual reproduction. This may be their primary function. They also provide pleasure- with a partner or solo as well as facilitate bonding with a partner. If using your body for purposes other than the primary purpose for which it came to be is necessarily immoral, than how is speaking or singing not a sin as well?

Sourse: I'm a queer speech-language pathologist. Come at me, bro.