Question: I have an idea that the seas of a world are red, not blue. However, the world should also be the birthplace of an intelligent alien species. Would it be scientifically possible to have a world with a red sea and where intelligent life can still develop?

Answer: 
Absolutely. [There's actually a sea on Earth which is red(ish)](https://www.livescience.com/32112-is-the-red-sea-really-red.html).

So it wouldn't take that much extrapolation to extend the algae planetwide and make it a brighter color. I'd think you'd want it to be loosely matted enough to provide flow of oxygen and sunlight, but that shouldn't be too hard to finesse.
The reason our own ocean is blue is because of the color of the sky. If your sky is red/orange, you might end up with a red ocean. You could also do what a couple others have said and try an alga that's red.