dat <- data.frame(ID = c(1, 2, 2, 2), Gender = c("Both", "Both", "Male", "Female"))
> dat
  ID Gender
1  1   Both
2  2   Both
3  2   Male
4  2 Female
For each ID, if the Gender is Both, Male, and Female, I want to remove the row with Both. That is, my desired data is this:
  ID Gender
1  1   Both
2  2   Male
3  2 Female
I've tried to do this by using the code below:
library(dplyr)
> dat %>% 
  group_by(ID) %>% 
  mutate(A = ifelse(length(unique(Gender)) >= 3 & Gender == 'Both', F, T)) %>% 
  filter(A) %>% 
  select(-A)
# A tibble: 2 x 2
# Groups:   ID [1]
     ID Gender
  <dbl> <fctr>
1     2   Male
2     2 Female
I'm declaring a dummy variable called A, where A = F if for a given ID, all 3 elements of Gender are present ("Both", "Male", and "Female"; these are the different values that Gender can take, no other value is possible) and the corresponding row has Gender == Both. Then I will remove that row. 
However, it seems like I'm assigning A = F to the first row, even though its Gender is only "Both", but not "Both", "Male", and "Female"? 
After grouping by 'ID', create a logical condition where the 'Gender' is not 'Both' and the length of distinct elements in 'Gender' is 3 i.e. 'Male', 'Female', 'Both' (as the OP mentioned there is no other values) or (|) if the number of elements is only 1
dat %>% 
  group_by(ID) %>% 
  filter((Gender != "Both" & n_distinct(Gender)==3)| n() ==1 )
# A tibble: 3 x 2
# Groups:   ID [2]
#    ID Gender
#  <dbl> <fct> 
#1     1 Both  
#2     2 Male  
#3     2 Female
Or another option is
dat %>%
   group_by(ID) %>% 
   filter(Gender %in% c("Male", "Female")| n() == 1)
# A tibble: 3 x 2
# Groups:   ID [2]
#     ID Gender
#  <dbl> <fct> 
#1     1 Both  
#2     2 Male  
#3     2 Female
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