I mean, you could argue that it is a vital mechanic that can't be excised. But it isn't... it doesn't do anything mechanically to the base rules that can't be ignored or removed. There's no "add +3 lawful points to your Strength" or "roll to hit from you Chaotic to-hit table".
It affects some spells? Spells can be added or removed at will. Swapping spells out of the list isn't even a houserule. If you want to do the legwork, change the spells. But even just purging them changes nothing. Casters don't get any reduced capabilities because some spells don't exist, they still get the same amount per day, and this already actually happens in some settings. Spells aren't base rules, spells are "stuff".
It affects some classes? Again, classes are not mandatory, even if they're called "Core Classes". Just remove alignment restrictions, or the classes altogether. Paladins already have a "code of conduct", simply put "don't do bad stuff" instead of "don't be Bad(TM)". If you don't want an Official List of Bad Stuff, just make add specific forbidden things to the list. Likewise, classes aren't rules, they're "stuff". Swapping classes in and out isn't a houserule either.
Monsters? Yeah, "stuff". Locations, planes, whatever.
You can still keep more tangible "axis", like Life/Unlife (positive/Negative energy) and just make up an Angelic/Demonic one for outsiders and planes if you want to keep them, and you're good to go.