This claim can be interpreted either way based on personal opinion. However, I think that the people who say this is true believe so because of the amount of laws that have been passed in recent years by Republican officials that some people say are anti-women and anti-LGBTQ.
Alexandria Ocasio-Cortez mentions that Republican officials have been targeting reproductive rights. Vanity Fair writes, "since Roe v. Wade was overturned in June, GOP officials all across the country have passed or put into effect extreme abortion laws, while conservatives in Congress have set their sights on a national abortion ban." Financial Times says, "Republicans risk voter backlash as they advance attacks on abortion," and includes examples of abortion laws that have been passed by Republican officials in the last years.
As for actions targeting LGBTQ Americans, the Washington Post writes that Republicans' openly critical behavior during Pride month is "part of a broader upheaval in which GOP-led state legislatures have moved to pass a record surge of restrictions on gay and transgender rights." CNN writes, "As they gear up for midterm elections, Republicans nationwide are intently focused on passing new restrictions on the LGBTQ community and, in particular, transgender kids." Some examples are mentioned: "[Republicans] have passed measures banning school instruction about queer people, outlawing gender-affirming care for those under age 18 and barring transgender children from participating in youth sports."
When looking at the abortion and LGBTQ restrictions pushed by Republican officials in the last couple years, I can see how people might agree with Alexandria Ocasio-Cortez that women and LGBTQ rights are being targeted.