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.
If you want a really exotic answer, perhaps your world has a [Fluorescein](https://en.wikipedia.org/wiki/Fluorescein) ocean. Fluorescein is in essence a complex carbohydrate, or in other words an organic compound, that naturally 'red-shifts' light, absorbing photons and releasing longer wavelength, lower energy photons as a result.

It typically exists as a powder, but can be dissolved in water or alcohol, though not all that well. BUT - imagine if you will a world in which your oceans first formed with a lot of this compound in them, and your first underwater plants used photosynthesis to break down this compound, producing just enough oxygen for their needs. They couldn't release excess oxygen as this would wreak havoc with the fluorescein, but let's just say that they could metabolise the fluorescein via an endothermic reaction triggered by sunlight (or some other energy source).

Because it's in solution, it's not that hard to evolve out photosynthesising animals that metabolise the fluorescein more effectively through being mobile, and potentially even evolve predation (although there would be less need for that in this environment because your organisms have evolved in soup).

The catch with this is that you are unlikely to have a great oxygenation event, and therefore far less likely to have land based creatures, but it's *possible* you could develop intelligent life in a fluorescein ocean, breathing their food and oxygen supply straight out of the water.