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.
***Your Ocean has a high hemoglobin content***

I would suggest using some sort of symbiotic system where said ocean thermally
convects hemoglobin to the surface where it absorbs Oxygen from the atmosphere.
This would create a bright red color. The convection along with the weight of
the molecule could then cause it to sink where a certain organisms in or on the bottom of the sea deplete the Oxygen where it will gradually turn a darker shade 
of red, at which time it will convect upward beginning the cycle again. An 
aquatic marine animal which has hemoglobin based blood and a special gland for absorbing the molecules would work. Perhaps the 'bloodfish' is responsible for,
or a result of this entire ecoaquatic system.