I don't think it is that clear in Sweden at least. Especially not if you just say birth control, i.e. what if I woman says she is on the pill and we have sex and it turns out she lied? I don't think she would get a rape charge.
I think it is also likely that someone in Sweden would get charged with a lesser crime than rape if it turns out they just removed the condom during sex. Having sex with someone that is sleeping and has not consented would be rape though.
EDIT: After having verified some more it he was not accused of rape for the condom thing. The rape charge is having sex with a sleeping person without a condom as it can be reasonably argued that she would not have consented to sex.
I know that the UK court which agreed to extradite him concluded that, under UK law, removing the condom was rape. But I'm not as familiar with the actual Swedish charges.
I don't know what else they may have concluded. But standard legal practice is to come to a conclusion about each charge regardless of what others you decided in case some of your conclusions are overruled on appeal.
For example if you conclude that either the condom or the sleep charge is sufficient, then the extradition can go forward even if the sleep charge got dropped.
Rape is sex with a person who does not consent. Period. What Assange is accused of is rape. Anyone who thinks otherwise should get a reality check and realize that there is no shade of grey here. Her body, her rules. Have sex without her consent, and that is rape.
Having sex without birth control with someone who didn't consent to that specific activity is legally rape in both the UK and Sweden. This is based on conditional consent, do something outside of the conditions under which consent existed, and you no longer have consent. More and more jurisdictions are recognizing this. Furthermore sex with someone who cannot consent due to being unconscious or sleeping is rape in a broader set of jurisdictions. (I do think that California goes too far by saying that you cannot consent in advance to being woken that way, but that is a different story. In this case there was no indication of consent given in advance for what he is accused of.)
So Assange is not being charged with some minor crime. He is being charged with rape.
Whether the charges would be pursued if he were someone else, well, that gets into selective enforcement. But this is at worst selective enforcement of a very reasonable law.