According to the very article you link to his wearing of a condom was only an aggravating circumstance, and not the primary reason for the charge of rape.

The primary reason was that he had sex with the woman while she was asleep, in a helpless state (in which she could not give consent).

Here's the full quote:

"Mr. Assange visited Sweden to give a lecture. He had sexual relations with two women there. In the home of the injured party, Assange deliberately consummated sexual intercourse with her by improperly exploiting that she, due to sleep, was in a helpless state. It is an aggravating circumstance that Assange, who was aware that it was the expressed wish of the injured party and a prerequisite of sexual intercourse that a condom be used, still consummated unprotected sexual intercourse with her. The sexual act was designed to violate the injured party's sexual integrity. Mr. Assange was accused of rape. Allegedly, the women agreed to sex on the condition Mr. Assange wear a condom. He did not do so throughout intercourse. Although the English courts had previously ruled that one cannot give conditional consent, in order to be able to allow extradition to Sweden, the Supreme Court ruled that his actions would constitute a crime under English law - thus allowing conditional consent to become valid in English law."

And to describe even just the aggravating circumstance described here as merely "not wearing a condom" omits that the reason for it being a problem: because Assange knew the woman would not have sex without a condom.

So (if true) there are 2 reasons to think he was having sex without consent, which is rape.

Yes, you did.

This entire idea that merely lying about who you before sex are constitutes rape is simply not true.

Certain deceptions may be crimes, but that is completely different.