Does choosing that specialization affect the story line? Will people hate me if I pick it?
It was originally planned for Wynne to call you out on being a Blood Mage while in the presence of Knight Commander Greagoir and First Enchanter Irving at the end of the Broken Circle quest. Dialogue was recorded, but was cut from the game. It can be seen in this fan-made reconstruction:
Wynne: Before we go any further, I would like to bring something up if I may.
Warden: (Persuade) They were not my spells. You are mistaken.
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Wynne: Oh, please. Credit me at least with the ability to tell different casters apart. I know what I saw.
Warden: (Persuade) The Grey Wardens taught me.
Wynne: But there is only ever one mage Warden at a time, and you are that mage. Who taught you?
Greagoir: I can believe that the Grey Wardens teach their recruits spells that would be…frowned upon by the Circle. Desperate times call for desperate measures.
Irving: The Wardens have many books reserved for themselves alone. They contain the wisdom of all Grey Wardens past and present, mages included.
Warden: Yes. That"s right.
Greagoir: The Grey Wardens" methods may be questionable, but I must believe their intentions are, ultimately, good.
Wynne: I hate to say this, but some of the things you were doing were hardly distinguishable from what those blood mages were doing.
Greagoir: This is a serious accusation, Wynne.
Warden: Everything I"ve done has made me better at battling evil.
Greagoir: Tell us now…are you a blood mage?
Warden: Yes, I am.
Greagoir: You know what happened to Jowan and you saw what they did to the tower.
Irving: It pains me to see you"ve fallen so far. You were strong enough without blood magic…
Warden: Why do you let the Chantry dictate the extent of your power?
Irving: It"s not about power, but respect for life—your own, and others. Do what you wish, Greagoir.
Because you did spare the tower, Greagoir then gives you the option to peacefully surrender and go on trial with the Chantry, with him saying that he will plead for the grand cleric to spare your life. The Warden can choose to refuse, which leads to Greagoir saying that you must be eliminated.
I imagine that this conversation was cut for two reasons. First, it creates a new outcome in which both the Mages and the Templars turn on you, meaning you don"t have either faction as an ally. Second, when you say that they are Grey Warden spells, Wynne notes that "there is only ever one mage Warden at a time" so you had nobody to teach you (with Irving reasoning that you learned from Grey Warden books). It seems that the developers decided they didn"t want to limit themselves in this way, so they cut the reference to it.
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Unfortunately, this means that in the final version of the game your allies, Wynne included, don"t seem to care that you"re using Blood Magic. However, you can accept this from a roleplaying perspective by imagining that you had an off-screen conversation and managed to convince your companions that they were Grey Warden techniques. If you go so far as to actually make Wynne a Blood Mage, then you can reason that she doesn"t fully recognize blood magic (since the only time she has seen it has been briefly during combat) and that she wants to believe the lie that you really are teaching her secret Grey Warden techniques.