Modern Rock has it 3, maybe even 4 phases, that have been friendly to female audiences.
The first one was 1981 - 1986, which was not long after Rick Carroll invented the "Rock of the 80's" format at KROQ, which eventually spread to several stations Carroll consulted, including 91x San Diego, The Quake in San Francisco, as well as several others. Denis McNamara had a similar impact on the East Coast with 92.7 WLIR Long Island, and WXXP Pittsburgh. Much of the MTV music of the moment, such as Duran Duran, were championed by these early Modern Rock stations.
The second was 1987 - 1993, which was when artists like Depeche Mode, R.E.M, Sinead O'Connor, Siouxie and Banshees and 10000 Maniacs dominated the format. Modern Rock, while still a small format, started expanding into new markets. Music by female artists, as well as melodic synth-pop, such as Erasure did really well on Modern Rock at this time. Many artists that went in to become core artists on Hot AC radio, such as Natalie Merchant, were initially only played on Modern Rock radio.
Third was 1994 - 1996, while some stations during this era started pulling entirely towards a male audience, others still tried to pull a 50-50 gender balance. Stations like Live 105 San Francisco, and 99x Atlanta, had their greatest successes during this time, while targeting a demo that leaned female.
On the other hand, some stations during this era, such as KDGE 94.5 Dallas, leaned exclusively female. KDGE in a lot of ways could be considered a proto Modern AC of sorts. For starters, the playlist was much tighter than your typical Modern Rock station of the time. Looking at old R&R playlists, the playlists of Top 40 Stations like KRBE Houston, Z100 in New York and KDGE were very similar. KDGE even played their top hits just as much as those stations, at 60 spins a week. KDGE heavily played music from the likes of Ace of Base, Real McCoy, and other pop artists of the day, while avoiding much of the harder rock music, such as Alice in Chains. The audio was also processed loud, as female listeners supposedly liked a sound that had a lot of bass.
The mid-90's was a time when a lot of melodic guitar pop started getting airplay on Alternative, then crossing over to pop formats. Gin Blossoms, Toad the Wet Sprocket, Barenaked Ladies and Goo Goo Dolls are examples of mainstream guitar pop from that era.
2011 - 2017 was another female-friendly era of Modern Rock. This was the heart of the indie-pop/ synthpop revival movement. M83, Lumineers, Florence and The Machine, Chrvches, Lorde and the 1975 are examples of melodic, female-friendly alt pop from that time-frame.