Three things off of the top of my head:
1.) They called them species and not races;
or
2.) They were unable to breed with each other;
or
3.) There was in-game lore that specifically stated that they were not races (i.e., if had been created in the fade or something)
Outside of those kinds of evidence, I tend to take what they say at face value. They call them races and they can interbreed (at least some of them are confirmed and we've no idea on the others either way). Seems to me that it's harder to make them species than it is to accept them as races.
1) From wikipedia
Many fantasy stories and worlds refer to their main sapient humanoid species as races, rather than as species.[19] J. R. R. Tolkien popularized the usage of the term in this context,[citation needed] and the use of races in the Dungeons & Dragons role-playing games further spread the label.[20] Many fantasy settings use the terms race and species interchangeably, such as the World of Warcraft computer game.
2) It is given that elves and humans can procreate (however, that also can be said of various different races in the real world), but the result has no physical traces of an elf. So common explanations of breeding and genetics do not work here.
I have seen no evidence that procreation of dwarfes and qunari works outside of their own race/species.
3) There is enough lore evidence that the elves, dwarfes and humans developed independantly and only met other races/species at a much later time. On the other hand, there is no indication in the lore that one descendet from the other.
Dragon Age is a fantasy world, and not all concepts that we know in the real world apply here. While it may be a squibbling over definitions, I think it's pretty obvious that the distinction between elf, human, dwarf and qunari is far greater than that between humans of caucasian, african and asian origin. Using the term "racist" refers in the real world to discrimination for of the latter. Applying it to somebody who is not comfortable of having sex with a member of another race/species in the DA setting is a very tacky use of the term.