From the wikipage on regeneration:
Whether Time Lords could change gender in regeneration was never addressed onscreen during the classic series and not explicitly focused on for much of the revival. In The Hand of Fear (1976), the Kartrian Eldrad compared his transformation from female to male to Time Lord regeneration, possibly suggesting the process could produce a sex change. The concept of Time Lords changing gender upon regeneration was seeded throughout Moffat's tenure as showrunner. In the second part of The End of Time (2010), the Eleventh Doctor (Matt Smith) briefly checks for an Adam's apple upon regeneration to confirm if he is still a man. In the 2011 episode "The Doctor's Wife", the Doctor recalls a Time Lord acquaintance known as the Corsair, who had at least two female incarnations.[33] In the 2013 short "Night of the Doctor", the Sisterhood of Karn offer a dying Eighth Doctor (Paul McGann) control over his inevitable regeneration, with "man or woman" being touted as possibilities.[34] The first on-screen cross-gender regeneration was shown in the 2015 episode "Hell Bent", in which a white male Gallifreyan general (Ken Bones) regenerates into a black woman (T'Nia Miller), who states that her previous incarnation was the only time she had been a man.[35]
The most notable Time Lord to have appeared in both male and female forms prior to Whittaker's casting is the Doctor's nemesis, The Master, portrayed from 2014 to 2017 by Scottish actress Michelle Gomez. This character was known as Missy, short for "Mistress".[36] In "World Enough and Time" (2017), the Doctor tells his companion Bill Potts, in reference to Missy, that Time Lords are mostly beyond gender norms and stereotypes; however, Bill points out that the males and females of the species collectively refer to themselves by a male title. From "Twice Upon a Time" onward, Jodie Whittaker portrays the Thirteenth Doctor, the Doctor's first female incarnation.
And if I dive even deeper in the fandom, then you come across that Time lords only a part of the Gallifreyian society.
And even deeper thoughts there are hints that the Doctor has reproduced sexually, and therefore the Gallifreyians are reproducing sexually. However other fandom say that Time Lords are cursed and cloning themselves.
A nice thought I found on the internet is that yes they are potraited as female and male. But do they have the sexual organs as we are used to see? For the 11th doctor has been nude, but the reproduction organs have not been shown.
(I also found a (almost disturbing) close up rant on the sexual organs, reproduction and birth of Time lords. The writer stated that they are hemiprodites and impregnated each other. However no sources were given for these facts)
And even more deeper (now we are at the bottom of Mariana trench). It is stated that everything is configurated when the Time lords are regenerating. So they always check if every body part is still there. But also internally everything is rewired. This also hints on that the brain is rewired. So they still have the memories of previous Doctors, but they also form new brain waves. And with that possibilities of different thought processes (for example how do I solve a problem and who do I fancy (read sexual atraction).
I think there is a beautiful hidden message in the regeneration of the Doctors. Whomever you are, whomever you have been, you will fall in love with just another. Even it is another species (o no another can of worms :D). So the duality between man and female is not there. They are both and at the same time they are either female or male.
(Sexual) identity, (sexual) atraction it is all a spectrum.
And last but not least, the Daleks are a hybrid between organic and mechanic. So what you hear is the machine talking. Apperently the programmer of the Daleks was a man :D. Well at least a Dalek with a deep voice. For all we know female Daleks could have had longer vocal chords.