TLDR:

Inertia. At one time, they were perceived as having the potential to cause harm, due to a mixture of then-valid reasons and simple paranoia. I don't believe that these represent the will of a god or gods (regardless of whether they exist) so much as a creation of man that has become almost completely dated and invalid in the modern world.

Wall of Text:

Because even if one assumed that a God or Gods are responsible for inspiring religious stories (that later become texts), they were still passed down via oral tradition for many generations before being put to paper. These oral stories were also written down by men, and going a step further, men were involved in determining which of the written stories would be accepted into the 'official' religious texts and which weren't- this process was referred to as the canon in the early christian church.

Ultimately, scriptures contain a mixture of the original ideas that inspired the stories and laws (whether or not a god exist) and ideas put forth by man.

The above is not an explanation; it's merely establishing the premises I'm working from with my later speculation.

Consider the many laws written down in the Torah- not eating certain foods, restrictions on sexual activity, etc. These seem quite ridiculous by modern standards and with the application of modern knowledge. Now, throw modern standards and knowledge out the window, and imagine for the moment that instead of being a large, worldwide religion, your entire culture is bound within a group of scattered, loosely associated, and generally small tribes.

Look at the foods that are specifically banned by the Torah- pork, meat with 'blood' in it (actually refers to the red juices released when rare meat is sliced; it is not in fact blood but many confuse this), shellfish, etc. Even with modern medicine, modern regulations on the food industry, and modern sanitation methods, people to this day still end up with health complications- even death- from eating shellfish, undercooked meat, tainted pork, etc. The risks are significantly reduced now, but not so much without any of those standards in place.

With a small tribe, there is a constant risk of eradication by another tribe, by disease, or any number of things. As such, much of what is an acceptable risk now given our methods and population carried a notable risk of annihilation for a small tribe.

This same idea carries over directly to sexuality; society at the time was male-dominated in a way that is rarely seen in the modern world- and violent. Most tasks were also performed by men, manually. As such, the mortality rate for the men was significantly higher than what we have now. Women too, for that matter, though their biggest killer was childbirth.

All sexual activity comes at some form of risk. Microtears frequently form in the penis, vagina, anus, etc. during sexual activity. These go largely unnoticed for the most part save for a mild feeling of soreness later, but are an excellent avenue for infection. As such, keeping the survival of the tribe in mind, there were very valid reasons for limiting sex to procreation as much as possible. Homosexuality, in addition to the omnipresent phobias associated with it, was poorly understood then even compared to now- while we now consider the idea ridiculous, there was no reason for men of that time NOT to believe that they could catch 'the gay' inadvertently. Mix phobia, misunderstanding, and an urgent need for the tribe to continue procreating as much as possible, and you've got homosexuality as a sin.

Because God says so. He is all powerful and can't be challenge. Do what he says or suffer.

A more interesting question: why deem something that harms no one as immoral. This is very simple for a christian but more complex and interesting for an atheist.