What is the condition called when someone believes that robots should be treated as though they are human?
The term robot humanization can be used to describe a psychological trait for considering certain robots to be human-like.
Life-like humanization of robots has been the aim of artificial intelligence (AI) research for many years, and we seem to be getting there with a robot called Sophia.

Using artificial intelligence, Sophia can communicate with people and even use facial expressions to convey emotions - and looks eerily human as she does so (ITV, 2017).

A YouTube video of a 2019 interview with Sophia on UK television programme This Morning can be seen at https://youtu.be/5_jp9CwJhcA
The pros and cons of AI being used to humanize robots have been debated for quite a while (Giger et al. 2019). One con is that the more a robot is humanized, the less likely people are to sacrifice it in favour of a fellow human (Nijssen et al. 2019).
References
Giger, J. C., Piçarra, N., Alves‐Oliveira, P., Oliveira, R., &amp; Arriaga, P. (2019). Humanization of robots: Is it really such a good idea? Human Behavior and Emerging Technologies, 1(2), 111-123. https://doi.org/10.1002/hbe2.147
Nijssen, S. R. R., Müller, B. C. N., van Baaren R. B., &amp; Paulus, M. (2019) Saving the Robot or the Human? Robots Who Feel Deserve Moral Care. Social Cognition, 37(1): 41 https://doi.org/10.1521/soco.2019.37.1.41
ITV. (2017) Meet Sophia, the eerily human-like robot... Retrieved from https://www.itv.com/goodmorningbritain/news/sophia-the-robot-freaks-our-piers-morgan-and-susanna-reid