If a board member has beliefs and values contradictory to core organizational values (written and developed by a board at some point) I pose that person should be removed. And, if the by-laws don't speak to a process that can ensure this action, modify the by-laws.
Sadly, when it comes to public school boards in particular, individuals can be elected to serve and despite what might be institutional values and/or the way such values are interpreted, individuals who might stand and speak against these values can actually get a seat. And, then, it is likely very difficult to remove them. That said, core values for an institution matter and a board member whose values differ from these should not be allowed to serve, in my opinion.
The Jewish "Independent" has posted a story about a public school where a candidate has declared that "Not all Nazis were bad". This coincidentally sounds like some other politician we know but let's put that point aside.
As you can see from the Independent article on the topic, this is not the only place where bias (?not contradictory to school values) drives the candidate and his platform. But what of citizens? Has the school board gotten it incorrect in their own statement of core values? Perhaps.....