The positions are not fundamentally opposed. You can believe that people have the right to choose their own leaders while also believing both that they should be accountable for that choice and that those leaders can be ignored or shunned if they do not follow the rules of the international community.

In other words, the only legitimacy that being elected democratically confers on leaders is that of being the authentic representatives of their people. The greater legitimacy of a government as a member of the international community of states might be influenced by whether it's democratic or not but is determined mostly by that governments actions and stated intentions. Hamas has refused to agree to steps, such as renouncing terrorism, that the US, EU and Israel believe are fundamental to a government being a member of the international community.

So they have accepted the results of the election, but they're under no obligation to be friendly with the result.

With that said, like all great powers the US's foreign policy is at times hypocritical to some extent. It will extol the virtues of rapid democratic change in some countries while discouraging it in others. This seeming mismatch in standards is the problem with a foreign policy with an idealistic rhetoric but a realpolitik reality. The truth is that encouraging rapid democratic change in all cases would be foolish and irresponsible, because it could lead to far worse outcomes than the status quo. Some countries can handle that kind of explosive change, others can't and need to be shepherded towards it at a slower rate. I think Egypt falls into the latter category.

Is it really that difficult to imagine that the US would turn a cold shoulder to organizations that recruit suicide bombers to blow up buses and pizzerias? Even if they win an election?