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: 
Sure. Just have a microorganism endemic to the seas that colours them red. Some sort of algae, maybe, that produces a red dye naturally as part of their life cycle. We kind of have that here on earth, manifesting as a [red tide](https://en.wikipedia.org/wiki/Red_tide) during algal blooms.

If the coloration is produced as part of the normal behaviour of the algae, rather than during oxygen-consuming blooms, you're good to go.
***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.