Is it permissible for a Salafi sister to attend an Eid party organized by deviant groups, with the aim of inviting new Muslim women, and what are the conditions for that?

There is no harm in attending a party with the intention of inviting and attracting new Muslim women, provided that the harm in attending is not greater than the anticipated benefit.

The benefits include saving new Muslim women from misguidance, achieving familiarity and closeness with them, demonstrating the truth, and fulfilling the duty of dawah (inviting to Islam).

As for the potential harms, they include: being perceived as agreeing with their views, inability to denounce evil acts, and being influenced by some of their misguided opinions.

A balance must be struck between benefits and harms. If the benefit outweighs the harm, then attendance is permissible, with diligence in clarifying the truth with wisdom and good admonition. However, if the harm appears greater, then withdrawal is obligatory.