Unfortunately, being aware that artificial forms of birth control are contrary to Church teaching doesn't necessarily mean that people know they're sinning if they use them. At least not in today's more secularized world, very sorry to say.
So they are doing much more damage to the authentically Catholic understanding of generosity and fruitfulness and "accepting children in whatever number God chooses to send them."
How is this so? What do they say to put out this message?
I disagree completely. The entire nation is aware that The CC is against contraception. Any Catholic who uses it is committing a grave sin, usually mortal. How culpable each person is we can't say, but that is true for any sin. As one poster has pointed out, there is no such thing as the "sacrament of ignorance". Just because people intentionally choose to remain ignorant of the truth does not let them "off the hook". The CCC #s 1740 and 1741 say that Catholics are under s serious obligation to form their consciences correctly. We are not talking of some obscure canon law that folks would not run into, but a fundamental truth that is critical to leading a holy life. Many of us are liable.
Some have said that Protestants as in the same boat. Meaning that, they too, are committing a mortal sin most of the time if they use contraception. The argument, I think, rests upon the natural Law.