The script:

# Installing required packages

if (!require("dplyr")) install.packages("dplyr")
if (!require("tidyverse")) install.packages("tidyverse")
if (!require("mapview")) install.packages("mapview")
if (!require("leaflet")) install.packages("leaflet")
if (!require("leaflet.extras2")) install.packages("leaflet.extras2")
if (!require("tidycensus")) install.packages("tidycensus")
if (!require("sf")) install.packages("sf")
if (!require("openxlsx")) install.packages("openxlsx")
if (!require("scales")) install.packages("scales")
if (!require("leaflet.extras2")) install.packages("leaflet.extras2")

library(dplyr)
library(tidyverse)
library(ggplot2) #From the tidyverse package
library(readr) #From the tidyverse package
library(leaflet)
library(tidycensus)
library(sf)
library(mapview)
library(openxlsx)
library(leaflet.extras2)
library(leafpop)
library(scales)

options(tigris_use_cache = TRUE)
options(scipen = 999)

# Getting the map data

ZIPList <- c("37016",
             "37026",
             "37095",
             "37118",
             "37149",
             "37190",
             "37037",
             "37060",
             "37085",
             "37086",
             "37089",
             "37118",
             "37127",
             "37128",
             "37129",
             "37130",
             "37131",
             "37132",
             "37133",
             "37149",
             "37153",
             "37167")

ZCTAMap <- get_acs(geography = "zcta",
                   variables = c(Under5_ = "B06001_002"),
                   year = 2021,
                   survey = "acs5",
                   output = "wide",
                   geometry = TRUE)

CountyMap <- get_acs(
  geography = "county",
  state = "TN",
  variables = c(Under5_ = "B06001_002"),
  year = 2021,
  survey = "acs5",
  output = "wide",
  geometry = TRUE
)
CountyMap <- CountyMap %>% 
  filter(NAME == "Rutherford County, Tennessee"|
           NAME == "Cannon County, Tennessee")


# Filtering and formatting the map data

RCMap <- ZCTAMap[ZCTAMap$GEOID %in% ZIPList,]

RCMap <- rename(RCMap, ZIP = GEOID)

ZIPMap <- mapview(CountyMap, zcol = "NAME",
                  legend = FALSE)+
  mapview(RCMap, zcol = "ZIP",
          legend=FALSE,
          col.regions = RColorBrewer::brewer.pal(9, "Greys"), alpha.regions = .5,
          layer.name = "ZIP Codes",
          popup = TRUE)


ZIPMap