I don't know if making Data female would have made him more well-liked. Like some of the posters explained above, there have been some examples of android/android-like women that haven't necessarily been more popular than Data as a male.
I think that a Data-like woman would have been seen as cold and unlikeable by the fan base, even if she'd have acted the same as Data (with the female version of a Brent Spiner). The women characters in Trek have a tendency to have to show "sensitive" sides at some point: Yar had her bruised past and friendship with Data and some sexy stuff, even 7 of 9 had to start "opening up." Kira Nerys ended up becoming almost soap opera-y gooey sensitive (just using the "stronger" women as an example).
And the men in Trek - "stronger" or not - don't have that tendency? Please name one man who did not have to show "sensitive" sides at some point
. Or a major male character who never did sexy stuff
I'd also like to ask you what the difference is between being sensitive and "sensitive", or stronger and "stronger", or what exactly does it mean being "soap opera-y gooey sensitive", but nevermind. Did it ever occur to you that these women showed that they had emotions not because they're women, but because they're people, and, well, most people have emotions?
As for Data - well he is an example of the above. He's an android who thinks he doesn't have emotions, but who's actually very "sensitive" with people, has strong friendships, feels a connection to someone he's only had a one-night stand in and who dumped him right afterwards (and later gets duped by her sister, because of the said emotional connection), feels an attachment to a furry pet, and most importantly, constantly wishes to become more human and find emotions. Oh, and he does some "sexy stuff" with Tasha, has a failed romance with another crewmember, and later does some more "sexy stuff" with a femme fatale-like Borg Queen. In addition, he has family problems with his android evil twin brother, becomes a "father" and loses the "child", finds a "mother" who turns out not to really be his mother (but he lies to her to spare her feelings), and finds another mentally challenged twin brother who turns evil. And he ends up sacrificing himself for his crewmates.
Sounds like there's no better example of your "sensitive", "gooey" and "soap-opera-y"
character than Data.
What would change if Data had been a female? IMO, nothing much. (Except that she wouldn't have a fling with Tasha.) He'd be just as popular as he is now, providing the actress was as good as Brent Spiner and played her the same way.