This is something that's only just started happening in the last few days ...
I use SendToReader to send posts from LiveJournal, and fanfiction from Archive Of Our Own, to my Kindle. For both these sites I am logged in, viewing a post, but when I click SendToReader on my toolbar I get a Kindle book that is the content that someone not logged in would see.
For LiveJournal it gives: "Adult Content Notice The content that you are about to view could contain adult concepts which may not be suitable for minors. To continue, you must confirm that you are at least 14 years of age"
For AO3 it gives: "Archive of Our Own ยป works show This work potentially has adult content. If you proceed you have agreed that you are willing to see such content ..."
I can still paste the text of a page [NOT the URL, just tried that and get the age-check messages] into the 'compose' screen on the sendToReader site -- but it was the one-click functionality that really hooked me on SendToReader and I'm sorry not to be able to use it any more.