Most OTL nations had a lot of tradition invested in uniform style and colour, but they all eventually ended up with drab colours suited for field life. A warexperience, like the British in the Boer War, usually advanced changes, and in nations not involved in war, like Denmark, light grey field uniforms with black greatcoats were retained into the 1940s. A Khaki uniform had been introduced in 1923, but the stocks of old uniforms had to be used before the men could be issued with the new uniforms. The officers were expected to purchase their own uniforms, so they often came in khaki, and the men in grey and black
A surviving CSA most certainly would have a lot of feelings for their "grey" identity, and I could imagine a grey uniform modfied well into 20th century. Basically you just need to minimise the bright colourpatches identifying service branch to narrow stripes, grey trousers and perhaps introduce a slightly darker/brownish grey tone. I guess it would not be that bad in relatively dry and warm climate like in the "CSA corner" of North America.
The WWII uniform of Germany is an example of a 20th century uniform retaining a lot of old traditions. Initially is so combined a relatively bright dark green tunic with dark grey trousers and with 19th century collar patches (looking like a Roman II numeral) on standing 19th century style collar and coloured stripes on shoulder patches indicating service branch. In the post war Bundeswehr any piece of equipment came in "Feldgrau" (fieldgrey) - a dark grey-brownish colour suited well for a "muddy" NW European climate - IMHO much better than the olive-green I was issed with in the RDA. Here just to point out, that there are alternatives to khaki and olive drab.
Anyway tradition could be kept in other connections than uniform colour. The service branch colours of the CSA - blue for infantry, red for artillery, yellow for cavalry etc. probably would be important, but less prominent on field uniforms, and the pockets flaps pointed in Austrian fashion could be another tradition bearer - no matter what uniform colour.
Regards
Steffen Redbeard