I think you might be overestimating how liberal the protesters were. Source: I was in Tahrir square during the protests and spoke with many Egyptians.

Almost all of the complaints I heard while I was in Egypt were about corruption and lack of opportunity. It was more frustration with rampant nepotism/cronyism and less a desire for liberalism. From the ground, it appeared to be driven by economic forces and not political ideology.

In fact, many Egyptian men that I spoke to made the argument for the continued oppression of women (e.g. the full burqa and absence from work). In general, the populace was decidedly anti-liberal.

The election of the Muslim Brotherhood happened after I left the country, but it was no surprise to me at all. The fact that they attempted to change the constitution so quickly after their victory was unwise, and the subsequent coup by the West was just as unsurprising.

And the UAE played a large role in covertly supporting the movement that toppled it.