I think washing detergent for white fabric can contain bleach, so the clothes will stay white and won't become grey. If this is the case, it'll gradually fade any colors of colored fabric.
And the other way around it won't keep the white perfectly white.
Dunno about the bleach part, that might be in some as well, but typically white fabric detergent contains optical brightener that counters the typical yellow tint of worn garments by emitting extra blue light (and your eyes perceive the full presence of the spectrum as white). That's also why this whitening effect will fade off if you then use detergent that doesn't contain brighteners: you are washing out those blue light particles once again.
Stuff formulated for whites specifically CAN contain things like bleach that can fade colors faster. Its not going to do it in 1 wash but cumulatively over time.
If it isn't specifically for coloured clothes, it contains optical brighteners, which fluoresce under UV light (like the sun) to make whites appear whiter. That's fine for light colours, but it makes blacks look greyish and dull.
New stuff should definitely be washed on it's own a couple of times, before being mixed in. New stuff can easily give off enough color to make a white shirt pink for example when washed with a red thing.
Just because you've been lucky or maybe have a lot of same colors where it doesn't matter doesn't mean it's a general rule to go by.
Apparently not specific enough: I use clothes detergent for all my clothes, but not detergent for colored clothes, I use regular clothes detergent for all my clothes
I'm a Luddite and old fashioned, using maybe 1/4 the detergent recommended, always use cold water, and use things like washing soda...and even I use detergents.
I dunno, general purpose works well enough. You can just add a little bleach if you need it for whites if you care. Oh and use powder of you can - liquid has way too much water in it, they're ripping you off.
Oh and use powder of you can - liquid has way too much water in it, they're ripping you off
Where I live, if you don't use the powder up in a month, it clumps or worse from the humidity. I swear by powder in the US Northeast. Here in Central America, I have to buy liquid.