summarise_all.R

library(dplyr, warn.conflicts = FALSE)
library(purrr)

expressions <- function(vars, funs) {
  
  #' make_expr("mpg", mean)
  make_expr <- function(var, fun) {
    expr((!!fun)(!!sym(var)))
  }
  
  names <- cross2(names(funs), vars) %>% 
    map_chr(paste, collapse = "__")
  
  cross_df(list(var = vars, fun = funs)) %>% 
    pmap(make_expr) %>% 
    set_names(names)
}

variables <- setdiff(names(mtcars), "cyl")
mtcars %>% 
  group_by(cyl) %>% 
  summarise(!!!expressions(variables, list(mean = mean, sd = sd)))
#> # A tibble: 3 x 21
#>     cyl mean__mpg sd__mpg mean__disp sd__disp mean__hp sd__hp mean__drat
#>   <dbl>     <dbl>   <dbl>      <dbl>    <dbl>    <dbl>  <dbl>      <dbl>
#> 1     4      26.7    105.       82.6     4.07     2.29   19.1      0.909
#> 2     6      19.7    183.      122.      3.59     3.12   18.0      0.571
#> 3     8      15.1    353.      209.      3.23     4.00   16.8      0    
#> # … with 13 more variables: sd__drat <dbl>, mean__wt <dbl>, sd__wt <dbl>,
#> #   mean__qsec <dbl>, sd__qsec <dbl>, mean__vs <dbl>, sd__vs <dbl>,
#> #   mean__am <dbl>, sd__am <dbl>, mean__gear <dbl>, sd__gear <dbl>,
#> #   mean__carb <dbl>, sd__carb <dbl>

Thanks for the help Romain. It seems to work even with a second grouping variable and adding min and max.
Unfortunately as with someone else's solution it doesn't work with my own data if my grouping variables are factors, but it does work if they're characters.