Is this the sort of thing you are looking for?
library(dplyr)
DF <- structure(list(ID = c(1001, 1002, 1003, 1004, 1005), `Current Date` = structure(c(1631491200,
NA, NA, NA, NA), class = c("POSIXct", "POSIXt"), tzone = "UTC"),
Date_1 = structure(c(1632096000, 1632182400, 1632268800,
1632355200, 1632441600), class = c("POSIXct", "POSIXt"), tzone = "UTC"),
Date_2 = structure(c(1317081600, 1317168000, 1317254400,
1317340800, 1317427200), class = c("POSIXct", "POSIXt"), tzone = "UTC")), class = c("tbl_df",
"tbl", "data.frame"), row.names = c(NA, -5L))
DF$Diff <- difftime(DF$Date_1, DF$`Current Date`, units = "days")
DF
#> # A tibble: 5 x 5
#> ID `Current Date` Date_1 Date_2 Diff
#> <dbl> <dttm> <dttm> <dttm> <drtn>
#> 1 1001 2021-09-13 00:00:00 2021-09-20 00:00:00 2011-09-27 00:00:00 7 days
#> 2 1002 NA 2021-09-21 00:00:00 2011-09-28 00:00:00 NA days
#> 3 1003 NA 2021-09-22 00:00:00 2011-09-29 00:00:00 NA days
#> 4 1004 NA 2021-09-23 00:00:00 2011-09-30 00:00:00 NA days
#> 5 1005 NA 2021-09-24 00:00:00 2011-10-01 00:00:00 NA days
DF_filtered <- DF %>% filter(Diff <= 7)
DF_filtered
#> # A tibble: 1 x 5
#> ID `Current Date` Date_1 Date_2 Diff
#> <dbl> <dttm> <dttm> <dttm> <drtn>
#> 1 1001 2021-09-13 00:00:00 2021-09-20 00:00:00 2011-09-27 00:00:00 7 days
Created on 2021-09-13 by the reprex package (v0.3.0)