However, apparently just because it's a safe day doesn't mean you won't get pregnant from unprotected sex.
Literal
However, safe-day [because-だからって], unprotected-sex even-if pregnant-not [quotative-という] reason is-not [apparently-らしいです].
~だからって (just because) dismisses a false assumption. ~というわけではない denies the inference: 'it doesn't mean that.' ~らしいです (apparently) hedges the claim as secondhand information. The stacking of these hedging and denial patterns creates a carefully nuanced warning.