!! or UQ evaluates the variable, so mtcars %>% filter(!!var == 4) is the same as mtcars %>% filter('cyl' == 4) where the condition always evaluates to false; You can prove this by printing !!var in the filter function:
mtcars %>% filter({ print(!!var); (!!var) == 4 })
# [1] "cyl"
# [1] mpg cyl disp hp drat wt qsec vs am gear carb
# <0 rows> (or 0-length row.names)
To evaluate var to the cyl column, you need to convert var to a symbol of cyl first, then evaluate the symbol cyl to a column:
Using rlang:
library(rlang)
var <- 'cyl'
mtcars %>% filter((!!sym(var)) == 4)
# mpg cyl disp hp drat wt qsec vs am gear carb
#1 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
#2 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
#3 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
# ...
Or use as.symbol/as.name from baseR:
mtcars %>% filter((!!as.symbol(var)) == 4)
mtcars %>% filter((!!as.name(var)) == 4)