The ligatures for != -> etc. are a terrible idea, imagine someone reading a programming language tutorial or a snippet and then actually trying to type stuff rather than copy-pasting.
-> now needs more internal “rendering” than → does.
Same with ≡ vs ===
Most languages only allow such symbols in strings, though, so it's pretty simple:
- Symbols outside of a string literal are ligatures.
- Symbols inside strings are the real symbol.
Ligatures are also rendered differently to any similar unicode characters.
The exceptions may be, as you said, online tutorials etc. with their own fonts and formatting, but I think that's more a part of the problem of bloated website design overriding browser-wide preferences.
For me ligatures are less important than syntax highlighting, but I do find them helpful - especially the greater-equal and smaller-equal signs are much more readable with ligatures, and that also applies when I read other people's code in my editor.