What effect does the ratio of the two have?
In and of itself, none. 200 ppm sulfate and 20 ppm chloride won't taste the same as 20 ppm and 2 ppm.
I understand that much. I get that any ratio is contingent on the values used. I guess my question is, after establishing your values for sulfate and chloride, does it really matter what the ratio of the two is?
I'm used to seeing it listed in the brewing water sheets, and I am sure that for different beers it varies, but is it an important variable to tweak or just a byproduct?
As good as "How to Brew" is, much of Palmer's info on water in that book is outdated, yet many still consider it gospel. That's where I think the pervasive use of the Cl:SO4
ratio in homebrewing comes from. Water treatment is much more complex than what he focuses on in that book.
Sulfate enhances a dry finish, which lends itself well to styles such as West Coast IPA that shoot for a dry hoppiness. Chloride is a flavor enhancer that tends to highlight malt, in particular giving it a bit of a fuller/richer quality. The two ions work independantly, and do not counter or "neutralize" each other, which is something that a ratio implies. All the ratio may
be helpful in is showing whether the particular balance of ions in that beer may be pushing a dry finish more than malty fullness, or vice versa. But even then, that's of minimal use because many styles can use a bit of each.
It's better to throw away the ratio altogether and focus on the two ions individually. You will likely settle on a particular ratio naturally, but that's mainly just a relic of looking at the two ions individually.