I remember being taught in school that the reasons why these two Abrahamic religions applied dietary laws was due. For example, pigs were prohibited because they eat important plants and carried parasites.
But, I felt like this was too easy of an answer to explain the origins of dietary laws in these two religions. Islam has a rule for slaughtering animals, but I can't see why any environmental reasons why this is necessary. Kosher rules in Judaism prohibit shellfish and the eating of milk and dairy together, and again, I don't think this theory applies.
Is there any evidence to support what I was told? Are there alternate theories for the origins of these dietary laws?
The parasite theory is voiced as far back as in the Babylonian Talmud. One of the cited rabbis voiced the opinion that dietary laws were out of date because the ovens in third century AD Babylon were significantly better than what was available to a nomad a millennium earlier on the plains of Moab.
I'm afraid I can't locate the exact passage but people practicing Reformed Judaism will likely know it since they often have to justify themselves to more conservative Jews.
You're analysis is correct, basically. There are certain laws that make sense from a health point of view, such as not eating pork for risk of parasites. This was the reasoning hypothesized by Maimonides, though he didn't know about parasites--he thought the reason was that pigs are unhealthy food and are dirty. He also thought that shellfish were bottom-feeders, that are also dirty and therefore unfit for consumption. There's another obvious example of unhealthy food that kashrut prohibits, which is scavenging from an animal already killed.
But, the rules do not fit into any coherent health system. It's possible that the author(s) of the bible thought that they did, but that reasoning is not explicit in the text. Ultimately there are many reasons people have suggested for biblical dietary restrictions, none with serious evidence. It's unlikely that one reason explains the entirety of the system of dietary laws, and it's also unlikely we'll figure out what those reasons are.