First of all, thanks to @Iroha for the huge help. The thing was that there were compatibility and support problems when using non-tidy functions with other tidy-functions, which led me to be quite confused (ik, rookie mistake :p).

Hence, to deal with the problem. you have to call the function with do.call() and recall the columns with pick(). The code fixed would be the following:

# Example df

ind <- c("A","B","C")
y <- c(2008,2012,2016,2020)
indiv <- rep(ind, times=4)
year <- rep(y, times=3)

a <- runif(n=12, min=0, max=100)
b <- runif(n=12, min=0, max=100)
c <- runif(n=12, min=0, max=100)
d <- runif(n=12, min=0, max=100)
e <- runif(n=12, min=0, max=100)
f <- runif(n=12, min=0, max=100)
g <- runif(n=12, min=0, max=100)

df_data <- data.frame(indiv,year,a,b,c,d,e,f,g)

# Code for max min and new range

newdf <- df_data %>% 
  mutate(Oldmax = do.call(pmax,c(pick(a:g),na.rm=TRUE)),
         Oldmin = do.call(pmin,c(pick(a:g),na.rm=TRUE)),
         Newmax = do.call(pmax,c(pick(e:g),na.rm=TRUE)),
         Newmin = do.call(pmin,c(pick(e:g),na.rm=TRUE)),
         Oldrange = Oldmax-Oldmin,
         Newrange = Newmax-Newmin) %>% 
  mutate(across(e:g,
                (((~ .x - Oldmin) * Newrange) / Oldrange) + Newmin,
                .names = "{.col}_bal")
         )

No need to apply it in the across one though, it is supported. Check info regarding do.call() function if you do not know how it works, it can be super useful even if you do not recall it all the time (like what happened in my case).

Hope anyone dealing with this kind of problems can find it useful :)