Majikthise, in the interest of complete transparency, let me say first of all that I run a dive shop on Phuket, on the Andaman (west coast) side of Thailand, and that some forum readers will have a knee-jerk reaction that it's for commercial interest only that I'm posting my own observations. However, professional integrity is important to me, and I believe that what I say is honest. Now that the caveat is out of the way....
July is indeed a month in the midst of the monsoon season here in the Andaman. Because the winds come from the southwest, the crossing from the mainland to the Similan islands can be very rough and dangerous. Only TWO marine parks, both in that area, are closed during this time of year. It's true, though, that these parks contain the very best diving in Thailand. You cannot visit these parks, but other marine parks ARE open for visitors, including the Phi Phi Islands Marine park, not too far from Phuket.
We dive year round from Phuket, and while our local dive sites are not, on average, as interesting as those in the Similans, they are still nice and you can enjoy good diving at them. One pleasant thing about diving our local sites during the summer months is that the boats are not crowded at all, and therefore the dive sites are not crowded either. Some of our shyer creatures, like leopard sharks, come back to the areas where we dive when there are fewer divers around flashing their cameras in the animals' faces.
In terms of weather, July is typically a fairly dry month of the "green" season (green because the rain greens everything back up). It doesn't rain every single day, and when it does rain, it doesn't rain all day long. Generally there will be a downpour of warm water (like standing under a shower) followed by bright sunshine that dries everything up. Sometimes there is chop on the ocean and a few people get sea sick at this time of year. We always have sea-sick tablets on board the boats, so it's generally not a big issue.
In a word, come. If you are interested in the Andaman Sea side of Thailand and you are not bothered that the prime diving area accessible from here is closed, we will do our best to help you have an enjoyable diving holiday. If given all that I've told you, you think you'd like to go elsewhere, I'll also tell you what I tell my own customers--consider Bali at this time of year. It's easy to get to, it's beautiful, and the mola-molas are just coming into season!