Not true. It's a teaching based on the natural law. It applies equally to all men of whatever religion. The prohibition of contraception is not specifically Catholic at all. Orthodox Jews have always found contraception fundamentally abhorrent. So did all 3 major protestant founders, each of whom wrote specific condemnations of contraception. Historically, Orthodox teaching did not even clearly distinguish between contraception and abortion, they were considered basically the same crime.
So to call this a "Catholic doctrine" is a fallacy.
Catholics may do well to learn the entire doctrine on sexual morals, but in the context of fighting abortion in a secular society (as opposed to persuading just Catholics) the issue of contraception should be put aside
This is fundamentally wrong and misguided, as well as a recipe for failure. Catholics can never put aside any part of their morality. "Fighting abortion in a secular society" is a pointless task if it requires one to ignore essential moral rules. It is pointless from a pragmatic perspective because one cannot "fight" one evil while accepting others. And pointless from a moral perspective because contraception will send you to Hell just as surely as abortion.
This is an absurd assertion on its face. Life in the real world requires constant decisions as to which real and perceived evils to fight and which to leave alone.