Q: Does the Action Bring Out Your Dead allow a player to trash New Rule cards from the center of the table?

or only Keeper and Creeper cards from in front of the player?

A: Bring Out Your Dead specifies that players may discard any cards from their hand or from the table in front of them. This is meant to signify only those cards a given player has control over. New Rule cards are not on the table in front of any one player – they are communal, so one player cannot decide to discard them using this action. (Neither may they discard Goals, for the same reason.)

Also note that it’s not only cards in play in front of the player, one can also choose to discard cards from one’s hand at the same time.