Ashildr and Harkness have more in common than long lifespans. Those two each have a type of immortality that was acquired unnaturally and from completely external sources. Also, they both occur in Nu Who.
Even if we assume that the young Doctor did choose to travel with immortals like Romana and Susan*, it was a young Doctor making that choice. Things have changed. Twelve has lived through horrors that his first seven incarnations had never known. He's a changed man, and it's not so shocking if we find that his opinions on this matter have also changed. If this question has an answer, we should be able to find that answer in Nu Who.
River is a special case. She's the Companion that, so far, has not travelled with the Doctor so much as she's made a habit of summoning him. The dynamic between these two characters is unique. I don't think we can learn about how Twelve views Ashildr by looking at River.
Twelve mentioned Harkness. Let's look at what Ten has to say on the subject:
It's not easy even just looking at you, Jack, 'cause you're wrong.
You are. I can't help it. I'm a Time Lord. It's instinct; it's in my guts. You're a fixed point in time and space; you're a fact. That's never meant to happen.
Harkness was, at first, an ordinary human being. Along the way, he lost the ability to die. In effect, an integral part of his nature was stolen from him. Ten can't help but see him as an abhorrent monstrosity. He is as disgusting to the Doctor as a zombie might be to you or me.
Ashildr's immortality suffers from the same weaknesses. It's just as unnatural. It's something that was done to her. Even more relevant, it was something that was done by the Doctor's own hand.
I think you're right. It's not simply immortality that the Doctor can't stand. We've seen Ten and Eleven wish for the companionship of fellow Time Lords and other long-lived creatures. The immense life spans of creatures that normally have such life spans don't seem to bother the Doctor at all.
Leaving Ashildr behind is just another example of the Doctor running away from a mistake that he can't fix. He can't stand travelling with her because she's the wrong kind of immortal. Taking her with him would mean that he'd have to face the mistake he made, day after day, without being able to make anything better. If anything, his company would make the mistake grow worse and worse.
And, maybe, her having human companions might make her better. After all, that's a technique that's worked for the Doctor himself, hasn't it?
* I'm not even sure that Susan was immortal. Oh, we can claim that Time Lords are immortal and we can claim that Susan was Gallefreyan. I don't think we can claim that all Gallefreyans are as immortal as the Time Lords.