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I basically agree with arguing that it makes sense to go accuse the right of promoting abortion by fighting contraception. I'm positive, though, that it's a mistake to limit this arguement -- that the right causes abortions -- to discussions of contraception.
The Republicans are forcing women, particularly women of color, to have abortions by pushing them into poverty. When the Republicans opposed universal health care in the 90's, they caused abortions. When Republicans oppose family leave, they cause abortions. When Republicans oppose increasing the minimum wage, they cause abortions. When Republicans support corporations that bust unions, they cause abortions. Poverty causes abortions and Republicans cause poverty.
I think this broader critique -- Republicans cause abortions by causing pregnancies (fighting contraception) and making those pregnancies unwanted (making it economically impossible to support children) is more likely to make inroads with working class Republicans than just arguing for contraception.
(It's worth pointing out that there are several prominent people who argue -- not entirely without merit -- that it's bad practice to suggest that abortions are bad. There are people who argue that an abortion is a medical procedure that takes place between a woman and her doctor and that it's inappropriate to attach moral weight to it, even when defending women's rights. I'm inclined to think of an abortion, when necessary, as being the best of bad options rather than morally neutral.)