Ligatures in coding fonts is a good workaround for giving people options on what they see. I personally dislike ligatures, but I work with people who do like them.
They want to see ≠, but typing ≠ instead of != in a shared code base is not going to happen, regardless of keyboard layout or language support.
It's unfortunate that keyboard input is an afterthought for most systems.
OS X is probably the best overall, with easy installation (with one gotcha for development) and SIL Ukelele being a decent editor.
XKB is tolerable, overcomplicated in some ways and limited in others (really needing a layout to be paired with an .XCompose), but Linux Desktops™ make it painful to configure any layout that doesn't ship with their system.
I use a great little Windows program called WinCompose[1]. It turns Alt Gr on my keyboard into a “compose” key, so I can press that followed by a short sequence of other keys to quickly type numerous common symbols. As a result, I can type “ or † or ≤ almost as easily as I can type " or * or <. Similar functionality is available on other platforms, and I expect anyone who was typing the same symbols frequently, as programmers do, would internalise the shortcuts for them in a matter of minutes.
Also built in to Windows these days is the Emoji (Soft) Keyboard which you can pull up with Win+. or Win+; (whichever you prefer). Since a few Windows feature updates back it even has a comprehensive math symbols section (under the Omega tab). It just needs a few more shortcuts under the math tab to make it really powerful. For instance, if you keep typing after you bring up the Emoji Keyboard it will search through Emoji and then replace your search word with your final selection, but it currently doesn't let you type search words or shortcuts for math symbols when you switch to the Omega tab.
Ligatures in coding fonts are a poor workaround for bad keyboard layouts. If you want to see ≠ then type ≠.
Julia is the only ‘major’ language I know that supports most such characters.