How often do job listings say they require a certain type of BA or MA, but they will secretly accept others?

For example, if a job posting for Architectural Historian, and it says you need to have a BA or MA in Architectural History, what is the likelihood that they’ll accept someone who just has a degree in History, but focused on architecture (but maybe a specific Architectural History degree wasn’t available to them at their institution)? Or who got a degree in History of Sexuality, but has since changed focus and still knows about and is totally competent with regards to architectural history?

Or do most employers pretty much throw out any resume that doesn’t exactly meet the criteria listed without checking to see if the candidate would actually be a good fit?