You've already stated it, parents can raise children to be critical thinkers in all subjects, including religion. A parent can tell a child their opinions on religion, but to present them as hard fact is not the same.
Polling on Catholic beliefs compared to their belief system:
http://time.com/6048/poll-catholic-beliefs-at-odds-with-vatican-doctrine/
I'm guessing some of this is based on not knowing the church's position or not understanding it on these issues. And some of it is that it's not primarily the beliefs that cause them to identify as Catholic.
And then just general religious knowledge:
http://www.pewforum.org/2010/09/28/u-s-religious-knowledge-survey/
This is focused on just one question:
http://nineteensixty-four.blogspot.com/2010/10/christian-belief-in-and-knowledge-of.html
Over half get it right, just barely, so it does make me wonder if most Catholics really understand much about their beliefs, and this is in a developed, wealthy country where people have time and resources to learn.
Most Catholics report occasionally or never go to church in the US, but many are likely to lie about it if they think the survey conductor is a person, pointing to social pressure once again being a big part as identifying as Catholic:
http://publicreligion.org/research/2014/05/aapor-2014/#.VR6llxj3arU
Many Catholic in the US are starting to less strongly identify as Catholics:
http://www.pewforum.org/2013/03/13/strong-catholic-identity-at-a-four-decade-low-in-us/
And unsurprisingly, that is leading to less and less Catholics in the US period, I think part of it is because fewer are indoctrinating their children into it. Even as native Catholic population loss is offset by Hispanic immigration, Hispanic immigrant children are less likely to identify as Catholic, likely because they live in a society where Catholicms holds less cultural and social power than where they came from.