I doubt that installing a JDK will adversely affect a yEd installation - we have like ten different versions of the JDK installed on our macOS test machines and yEd runs just fine.
You could try to run yEd from a terminal/console for debugging purposes, though. To do that, open a terminal and enter
[path/to/java_home]/bin/java -jar [path/to/yed_install_dir]/Contents/Java/yed.jar
[path/to/java_home] is usually something like "/Library/Java/JavaVirtualMachines/jdk-11.0.1.jdk/Contents/Home".
[path/to/yed_install_dir] is usually "/Applications/yEd.app".