If my sister doesn't know the Church's teaching on birth control, do I have any obligation to tell her? If so, is that judging?

We make judgments all the time. We judge what is right and what is wrong. What we must not judge is the condition of another’s soul or its destination. That is because an act that concerns an objective evil is only one condition of mortal sin. There must also be full knowledge and full consent; otherwise the culpability for the sin may be diminished. Only God knows for sure.

"Indeed love itself impels the disciples of Christ to speak the saving truth to all men. But it is necessary to distinguish between error, which always merits repudiation, and the person in error, who never loses the dignity of being a person even when he is flawed by false or inadequate religious notions. God alone is the judge and searcher of hearts; for that reason he forbids us to make judgments about the internal guilt of anyone" (Gaudium et Spes 28:2).

It is never permissible to leave a someone in a state of ignorance concerning grave matters of faith and morals, for Christ commanded us to preach the gospel to all creatures and to teach them "to observe all that I have commanded you" (Matt. 28:20). Prudence requires, though, that you choose the appropriate manner, time, and place.