Here is a dplyr solution
library(dplyr)
library(stringr)
Censor_consistently <- function(x){
str_replace(x, '^\\s*([<>])\\s*(\\d+)', '\\1\\2')
}
test_df <- tibble(x = c('0.001', '<0.002', ' < 0.003', ' > 100'), y = 4:1)
mutate_all(test_df, funs(Censor_consistently))
# A tibble: 4 × 2
x y
<chr> <chr>
1 0.001 4
2 <0.002 3
3 <0.003 2
4 >100 1