Who decides a university's stance on a topic?

Universities work like any organization. The stance of the organization is the stance of its leadership. It can be the president, the chancellor, whatever you call it, it can be the board of directors, it can be the faculty assembly… It can even be a university-wide poll as you suggest. It depends on how the university is governed.

The statement "organization X has position Y" is a very common one in English. For example, "country X is a friend of country Y". "Statistically", it's unlikely that every single inhabitant of country X is actually a friend of every single inhabitant of country Y. Saying that a group of people does something is not the same as saying that every single member of that group does something.

Universities have a governance structure like any other other institution, company or country. For issues of this type, most universities have a committee for diversity and inclusion (example 1, example 2, example 3). The people in this committee design (suggested) policies and measures on the topic. Depending on the university and on the extent of the measure, most nontrivial changes of policy will have to be approved by the governing body of the university. The names and tasks of the different governing boards vary by university. For example, information about the governing structure of UCL can be found here.