2. Know your audience.
If the topic is really touchy (and unrelated to your tour theme in general), you’ll want to read the room before diving in.
In a previous job, we ran tours in Washington DC where guides actively led discussions about politics (those guides are heroes, in my mind). It worked because the guests had actively signed up for it, knowing ahead of time what they were getting into.
To give you an example, one of my tours used to pass an NYC courthouse famous for “City Hall Weddings”. Occasionally, during the year that the Marriage Equality Act was passed, a guest would ask me about LGBTQ+ marriage in NYC. Whether or not I would go into the discussion of marriage equality in NYC with the guest would depend entirely on how they asked the question, or what question they asked.
I learned that “Do you believe gay marriage is ok?”, asked in front of the entire group was usually asked by someone who didn’t approve of it and was looking to debate anyone who did. In this case, I would usually make a comment about personal opinions not being relevant now that the law was passed and quickly divert into NYC’s history of civil rights (moving into safer topics).
However, if someone can up to me while we were walking and asked if LGBTQ+ marriage was legal, I would be happy to go into the law and the LGBTQ+ Rights Movement in NYC.