Solution: You are likely trying to connect to a standard Java server. You need an Eaglercraft proxy. Use the server JAR provided on GitHub, or search for "Eaglercraft 1.8 public servers."
Unlike the earlier "Eaglercraft 1.5.2" (which was based on the stripped-down "Classic" version of Minecraft), EaglercraftX 1.8 is a port of the modern, fully-featured game.
EaglercraftX was developed by lax1dude and represents a significant technical achievement in software porting. The project involved a complete rewrite of the Minecraft 1.8 source code using TeaVM, an ahead-of-time compiler for Java bytecode that translates the code into JavaScript.