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 the oceans contain very high concentrations of iron, in the form of rust, it would create a red ocean. 

This environment would be ideal for [rust-eating microbes](http://www.nbcnews.com/id/40533835/ns/technology_and_science-science/t/new-species-rust-eating-bacteria-destroying-titanic/), which could form the base of oceanic food web in the same way photosynthetic plankton form the basis of our aquatic food webs. 

What implications this has on your world's plant and animal life is outside the reach of my familiarity with biology, but I don't think it would necessarily preclude the development of intelligent lifeforms.