Gender politics in Ancient Egypt is a difficult topic made only the more complicated by the adoption of figures such as Hatshepsut into the gender studies cannon. The sources for how female Pharaohs were perceived by Ancient Egyptians are limited to the representations created in their lifetime as part of the dissemination of their image and in some notable cases, the post-mortem reaction to their images.

The idea of female Pharaohs being interpreted as male in gender is a long-standing one academically but the influx of 3rd wave feminism into academia has had some significant impact on this argument. The more modern argument is that Pharaohs were not overly concerned with gender but their representations in statuary and relief were aimed at likeness to deities or at androgyny. For instance this depiction of Hatshepsut is not presenting her as a man but as Osiris. This one in the Met is variously seen by scholars as feminine (note the mouth and the smile lines on the eyes) or masculine (the nemes headcloth and masculine physique) but due to both characterisations is demonstrably androgynous.

As for how Ancient Egyptians perceived this gender neutrality from their Pharaohs, the issue is discoloured by the political situations in which the key players came to power. Hatshepsut's name suffered a damnatio memoriae after her death during the reign of Thutmosis III. Her cartouch was scrubbed out where it was accessible, her name removed from the king lists, her statues broken up etc. One explanation formed from western interpretations of patriarchy is that this is a reaction against her usurping a traditional male role. Curiously though the evidence indicates that this destruction of her memory took place very late in the reign of Thutmosis III after he had already proved himself a successful and powerful Pharaoh. The delayed reaction doesn't make sense with the sexism scenario but implies something more political, perhaps to do with his successor Amenhotep II. Tausret's name was similarly damaged by her successor Setnakht but there are strong indications this his succession was forceful i.e. Civil War. I think given the unique artistic style of the Amarna period we can include Akhenaten in this - the class master at androgyny - and obviously his name removal can be any number of factors from his movement of the capital, rejection of the Thebaid, iconoclasm etc. The sexist interpretation is tempting but simplistic in many of these scenarios. Essentially we have very little evidence that Ancient Egyptian even cared about the gender of female Pharaohs aside from the Pharaohs themselves chose to present.

The lifestyle of a Pharaoh is similarly complicated by royal representation and iconography. There was a code for Egyptian art, a regimented tradition which defined the borders of acceptable style. This code evolved over the whole course of Ancient Egyptian history from its roots in the Pre-Dynastic period. In general this schematic for royal representation was based on the Pharaoh being male - perhaps a reason for the androgyny inherent in later periods when Pharaohs wanted to be seen as more than just the normal King, a deity, but were restricted by this artistic code. A couple of millennia further on, when we can view artistic production of the entirety of Ancient Egyptian civilization in a single museum or even a website, we have a majority representation of men doing activities and thus creating for us an assumed gender role for Pharaohs. When a female Pharaoh comes along and takes part in fairly typical construction practices or uses the same forms and presents herself carrying out similar activities we conclude she is assimilating a male gender role. Female Pharaohs didn't live as men, they lived as Pharaohs and their kingship the foremost aspect of the presentation.

EDIT: this answer has been playing on my mind since I wrote it, namely I fell into the same trap I identified. I made a mistake in attributing the nemes headcloth to being masculine whereas it is only so because in the statistical sample we have available, it is worn mostly by men. The hat itself has no gender, it's gender is a modern creation from what we can see of the ancient culture and artistic style.

You may be interested in this answer. Female Pharaohs were depicted as men, but they weren't actually thought to be male--feminine pronouns were invariably used for them.

An important point to make, that lucaslavia touches on, is that the OFFICE of pharaoh in ancient Egypt was male - as in, the pharaoh was inherently masculine because of the gendering of their language. The person of the pharaoh could be either male or female in their private life, but when they were occupying the office of the pharaoh/performing the duties of the pharaoh, the language required male pronouns.