There are several studies that reveal sexist, capable, racist tropes, etc. in this or that role play. (See the bottom of the publication for some references.)
How does it affect the participants to play such games? As everyone has an opinion and not all are beautiful, The answers should be based on rigorous studies..
Some common opinions on the matter:
- Playing games is fun and therefore the question is diverted.
- Only stupid and worthless people are affected by the means they consume.
- Playing a game with orcs does not cause changes in behavior towards any minority.
- Playing a game with orcs reinforces racist stereotypes and thinking.
- Playing a game with sexist stereotypes reinforces patriarchy and, therefore, has all kinds of unintended consequences.
To distinguish what is true or not, experimental studies are required. A study of other media could be useful, if the answer also rigorously argues how and to what extent it is generalized to role-playing games.
The connection between violent video games and aggressiveness has been studied from several angles. From what I understand, the state of the art is that if violent games have an effect, it's positive but very small. There can also be no effect.
Certainly, there are methods to quantify biases and stereotypes, so it would be possible to conduct similar studies on them; The question is whether something has been done and what they say about RPGs.
I have read several studies, such as the ones mentioned below, but I do not remember having addressed them in this question. I talked about this with someone who was writing a master's thesis about sexist and drunk tropes, and they did not know about such studies, although they had not investigated it. This does not seem to be a common question, for some reason.
I follow an international magazine of role-playing games, analog game studios and, more recently, Games and culture, but I do not remember articles related to this, but you may forget something and have not read your files in detail.
I have not examined the broader literature on game studies, nor have I read most of Solmukohta's books.
Research articles, some of them unfortunately behind a payment wall:
García, A. (2017). Privilege, power and Dungeons & Dragons: how systems shape racial and gender identities in tabletop role-playing games. Mind, culture and activity, 24, 232-246. https://www.tandfonline.com/doi/full/10.1080/10749039.2017.1293691
JONES, Shelly. Blinded by the roll: the critical failure of disability in D & D. Analog games studies, 2018. http://analoggamestudies.org/2018/03/blinded-by-the-roll-the-critical-fail-of-disability-in-dd/
Stang, S., and Trammell, A. (2019). The ludic bestiary: misogynist tropes of the female monstrosity in dungeons and dragons. Games and culture. https://doi.org/10.1177/1555412019850059
STENROS, Jaakko; SIHVONEN, Tanja. Outside the dungeons: Representations of queer sexuality in RPG source books. Analog games studios, 2015, 3. http://analoggamestudies.org/2015/07/out-of-the-dungeons-representations-of-queer-sexuality-in-rpg-source-books/
Trammell, Aaron. 2014. "Misogyny and the Female Body in Dungeons & Dragons". Analog games studies 1 (3). http://analoggamestudies.org/2014/10/constructing-the-female-body-in-role-playing-games/