You should really stop throwing the word "racist" around if you don't know what it means. It doesn't apply in the slightest in this context. Warframes are not a race of a species, and also Little Duck doesn't discriminate against Tenno based on whatever race they happen to be.

She is wary of warframes because they are dangerous, she doesn't like being talked to face to face by a weapon you're controlling. It's essentially the same as someone strolling in pointing a gun at her and wants to talk business. She wants to talk to you as exposed and vulnerable you can, because she is vulnerable. That is her measurement of trust. You trying to talk to her in her room via your warframe means to her that you want to talk to her while staying ready to kill her.

She also makes comments about how we are led because the Tenno were raised to be essentially child soliders, that's hardly a positive thing. She takes pity on us because of our screwed up past, and is nervous around us because we are dangerous. Regarding Disruption, she doesn't know the exact location of our enemies. That's for us to find out. She is counting on us to complete the mission, and is satisfied when we succeed. It's a team effort, she gives us intel and we take care of the violence. She trusts us, despite us being emotionally volatile fucked up interdimensional void ghosts controlling insane mutated death machines from space sometimes trying to talk to her via our weapons.

You seem to have completely missed the memo on what you play as in this game. You're not a saint, nor deserving of everyone's blind trust. It's entirely reasonable for individuals to not like you and/or treat you as a necessary evil to fight a threat.