Do you differentiate between Jews and non-Jews in a synagogue? For example, in seating, or in things that are prohibited to do?
It is uncommon for non-Jews to attend services in a synagogue, and the only ordinary case is a non-Jew studying for conversion, who attends services as training for after his conversion. On the other hand, there is no prohibition for a non-Jew to enter a synagogue, for the sake of prayer to God (see a previous post on this here: https://dinonline.org/2011/01/27/a-non-jew-in-the-synagug/
There is no “segregation” between Jews and non-Jews in the synagugue, however, most synagugue “functions,” such as being called up to the Torah, officiating as “cantor” (to lead the services), and so on, can only be performed by Jews.