The United Methodist Church over in the USA doesn’t seem very “evangelical” to me. They aren’t eager to bring guests to the covered dish dinners. It has its share of libs and Dems and seems to be the denomination with the most school teachers. Southern Baptists would fit the “evangelical” description better IMHO; however, there aren’t many liberals I know of who are Baptists.
You are right but when these denominations came into existence in the 18th century they were the Evangelical movement of the time. Somehow churches like the Methodists lost their way and stopped preaching and instead became too enamored with taking up the latest lefist cause.