And on that note the Galileo affair was an aberration—it'd be unwise to see it as exemplary of the Church's general attitude towards unorthodox science.

For instance, most instances of heresy were crushed successfully without them bearing fruit or gaining influence. (In some part because most incidences of heresy are actually false theories. Because most new ideas in general are wrong.) The Galileo incident was an epic failure of both religious meme enforcement and public relations. It hasn't happened often! Usually the little guy loses and nobody cares.

(The above generalises beyond "The Church" to heavy handed belief enforcement by human tribes in general.)