Questions: In the 1990s, challenged established notions that LGBTQ legitimacy could only come through assimilation into mainstream heterosexual society.

The answer is: New Queer Cinema.

Explanation for each option:

1. New Line Cinema: This is a film production studio known for producing a variety of mainstream and independent films. It is not specifically associated with challenging notions about LGBTQ legitimacy.

2. New Queer Cinema: This term refers to a movement in queer-themed independent filmmaking in the early 1990s. Filmmakers associated with New Queer Cinema, such as Todd Haynes and Gregg Araki, challenged the idea that LGBTQ legitimacy could only be achieved through assimilation into mainstream heterosexual society. They often explored themes of identity, sexuality, and resistance to normative cultural standards.

3. New Direction Cinema: This is not a recognized term or movement in film history, particularly in relation to LGBTQ themes.

4. Equality Cinema: While this term might suggest films promoting equality, it is not a specific movement or recognized term in the context of 1990s LGBTQ cinema.

Therefore, the correct answer is New Queer Cinema, as it directly relates to the movement that challenged established notions about LGBTQ legitimacy during the 1990s.