Is it permissible to absolve oneself of responsibility for something that is partly permissible and partly forbidden, such as giving a toy that plays music, or selling PlayStation points through which the buyer can purchase a game that violates modesty? And does the seller incur sin as a result?

It is not permissible to gift a toy to someone if it is known or highly probable that they will use it for impermissible purposes. If there is no such knowledge or strong probability, then the prevailing custom in society should be considered. If it is customary to use it for impermissible purposes, then it is not permissible to gift or sell it; otherwise, it is permissible. The phrase "absolving oneself of responsibility" is not sufficient in this case, as the decisive factor is the knowledge or strong probability of how the recipient will use the gift.