This is what is known as a 'slippery slope' argument. In other words, arguing that a step in one direction will inevitably lead to an unstoppable slide to something much more extreme. I rarely find slippery slope arguments convincing, personally, and think that they're a somewhat hysterical way of dealing with issues that people don't really understand.
Homosexuality has been accepted to various extents in different societies throughout history---the ancient Greeks, some Polynesian cultures, the example of 'hijras' in India (and to a lesser extent Pakistan), etc. In none of these examples is there a correlation with incest. Incest has generally always been much more taboo universally than homosexuality, but there have been a few societies where it is practiced---among the ancient Egyptian pharoahs, for example, the royal family often married siblings. But again, there's no reverse correlation with homosexuality.
The argument above for me seems like a vegetarian arguing that if you're willing to eat chicken, then next thing you know you'll be eating street cats. Or someone arguing against allowing women to vote, because next thing you know people will start demanding the vote for dogs. Slippery slope arguments are emotionally engaging but I don't find them logically persuasive...