That sounds strange, that feature works for me.
There are 3 things that might be the problem
1) There are 10 cards from the base set that you cannot "unfamiliarize" yourself with: Chapel, Festival, Gardens, Laboratory, Market, Moneylender, Smithy, Village, Witch and Workshop.
At the start of this Online implementation the developer found that too many players couldn't play any game because by mistake they made themselves unfamiliar with all or almost all cards, so less than 10 remained.
If the cards you don't want are from those 10 cards, that would explain the behavior, and unfortunately there is nothing you can do (I'm not sure if changing the above behavior of the 10 cards would help now overall).
2) If you create a manual table, or maybe you end up on such a table after playing against a human opponent, then the table option "Respect familiar cards" may not be set. You can set it by going into "Edit Otpions" in the end-of-game screen, then "Advanced Options". If there is no checkmark besides "Respect Familiar cards", click the box so it contains a checkmark. Then familiar cards should work.
3) In the "Options" tab, there is a setting "Max unfamiliar cards". If the value there is greater than 0, (2 is the default, I think) then you allowed the game to put at max that number of unfamiliar cards into your kingdom. Set this value to 0 and it will not do this any more.