While the advent of the Women's Rights Movement of the 60's (it was not the first one, it's just the one everyone remembers) did help further the availability of abortion and contraception it is not solely responsible for it.
I was talking about the wider history of the advancement of Women's Rights the feminism of Wollstonecroft in Revolutionary France; the greater degree of personal and romantic autonomy provided by the Industrial Revolution; the Suffragist Movement; the Sexual Revolution of the 1920's; women entering the workforce in the 1940's; the Woman's Movement of the 1960's and 70's; and so forth.
[The decriminalization of homosexuality] started in the late 18th century, indeed quite a few European countries and half the America's made it legal before 1950.
The history here is very uneven across the world, but one thing that (AISI) ties them all together is that this advancement gay rights has almost been tied to the changing gender and family philosophies of the times; whether it was Revolutionary France, Weimar Germany, or 1960's* America, in the past few centuries, each of these advances came in the context of greater personal, political, and/or sexual freedom for women.
The availability of effective contraception was limited by ability to produce, however once it (via condoms and the pill) became mass produceable it took off very quickly, despite opposition.
The rise of effective birth control was itself tied inexorably to the causes of women's personal and sexual freedom; research and development of various contraceptive advancements were as much or more motivated by gender politics as by profit. Though speaking of which...
While the re-legalization of Abortion was driven by Women's Rights Movements, it has historically been legal in most of the world off and on.
Okay, I may have over spoken with abortion; the rise of the anti-abortion movement in the US, which was initially motivated by concerns of a "diminishing white race", transformed into an attempt to rollback growing female sexual freedom, before tagging on "pro-life" justifications, complicates the narrative of growing women's rights advancing each of the issues in the OP.
*Illinois was the first US state to repeal sodomy laws in 1962