I've read a lot of people complaining that there are no "ordinary people" or "normal people" as companions in the Moffat era, but I think that most (if not all) are, I mean they are all normal with something that makes them special, but they all started being very normal (clara, rory and amy). I think that when people say they want to see someone "normal" they refer to their definition of normal, there are as many ideas of what a normal person is as as there are people in the world
Yes, it's really subjective. I mean, I don't think I necessarily can empathise a lot here, because a lot of times what people seem to mean with regards to the RTD era is "normal like me". You see that in a lot of the relatability discussions as well, "ordinary, so I can relate to them". Which is a mindset I can't seem to put myself into.
Clara, Amy and Rory, at their core, aren't less "real" than any RTD companion. They all did extraordinary things happen to them (Rory being brought back to life as a Auton) or achieved extraordinary feats (Clara choosing to scatter herself through time), but this is almost a requirment for someone travelling with the Doctor. In Amy's case, this might have happened during childhood, but that little girl that this happened to was a normal child. And while she's consistently portrayed as someone different from her surroundings, that's hardly something which doesn't happen in everyday life.
But really, what's the problem here? Why is this fandom so hesitant to accept anyone who doesn't fit into their own narrow conception of what it means to be normal? The longer I spent on this website, the more I think this approach is something which deserves to be challenged, rather than appeased. Maybe it's truly time to bring on companions from the past or the future, from alien planets, companions who aren't human.
Because it's starting to become mildly disturbing that people seem to think it's only possible to care when it's someone like you on the screen. That isn't even true in a Doctor Who context - we all seem to be perfectly fine with the Doctor. But as soon as it's a female companion on screen, the idea that she might not be someone's particular brand of 'ordinary' appears to be offensive. (And isn't it just interesting that Jack seems to be accepted where River isn't...) Make of that what you will.