The New Launcher is incompatible with the version of MacOS that is currently running so I used this (https://bugs.mojang.com/browse/MCL-5654) thread issue to fix it for when the new launcher came out. (I wasn't sure whether to post this under the New Launcher or the Java version). By the way, this fix mentioned above works for 1.12 and lower, so I'm not sure what was implemented to make it crash after clicking these buttons.
However the newest update 1.13 (using the workaround stated above) opens to the main menu, but doesn't allow Either Single player or Multiplayer to be opened (Options can be clicked, however it promptly crashes afterward, or if any other button is selected). The executable file crashes stating "java has quit unexpectedly" with this in the Problem Details and System Configuration.
Process: java [26044]
Path: /Library/Internet Plug-Ins/JavaAppletPlugin.plugin/Contents/Home/bin/java
Identifier: java
Version: 1.0 (1.0)
Code Type: X86-64 (Native)
Parent Process: java [25892]
User ID: 503Date/Time: 2018-07-19 11:33:35.082 -0400
OS Version: Mac OS X 10.8.5 (12F2560)
Report Version: 10Interval Since Last Report: 4446962 sec
Crashes Since Last Report: 989
Per-App Crashes Since Last Report: 16
Anonymous UUID: 7F2C7753-09EF-0A66-ACF4-90B82C4C0321Crashed Thread: 26 com.apple.audio.IOThread.clientException Type: EXC_BREAKPOINT (SIGTRAP)
Exception Codes: 0x0000000000000002, 0x0000000000000000Dyld Error Message:
Symbol not found: ___sincosf_stret
Referenced from: /Users/USER/Library/Application Support/minecraft/*/libopenal.dylib
Expected in: /usr/lib/libSystem.B.dylib
Fixed by updating to macOS High Sierra