When attempting to run /log counter white,black I get the following error:

[14:29:07] [main/INFO]: [CHAT] [14:29] Expected whitespace to end one argument, but found trailing data
[14:29:07] [main/INFO]: [CHAT] [14:29] ...nter white,black<--[HERE]

Subscribing to a single counter works as expected.
I am running minecraft 1.16.5 and doing a small amount of testing seems to have revealed the issue has been in carpet since 1.4.25.

Due to extra arguments for this call, the format cannot accept comma character and you need to quote it properly. The command suggestion is right. Use /log counter "white,black" now