library(dplyr)
filter_all(dat, any_vars(. != 0))

#       A-XXX  fBM-XXX    P-XXX  vBM-XXX
#1 1.51653276 2.228752 1.733567 3.003979
#2 0.07703724 0.000000 0.000000 0.000000

library(tidyverse)
dat %>% rownames_to_column() %>% filter_at(vars(-rowname), any_vars(. != 0))
#         rowname      A-XXX  fBM-XXX    P-XXX  vBM-XXX
#1  BATF::JUN_AHR 1.51653276 2.228752 1.733567 3.003979
#2 BATF::JUN_CCR9 0.07703724 0.000000 0.000000 0.000000

library(tidyverse)
dat %>%
    reduce(`+`) %>%
    {. != 0} %>%
   filter(dat, .)
#       A-XXX  fBM-XXX    P-XXX  vBM-XXX
#1 1.51653276 2.228752 1.733567 3.003979
#2 0.07703724 0.000000 0.000000 0.000000

dat %>%
  rownames_to_column('rn') %>%
  filter(rowSums(.[-1]) != 0) %>%
  `row.names<-`(., .[['rn']]) %>% select(-rn)
#                   A-XXX  fBM-XXX    P-XXX  vBM-XXX
#BATF::JUN_AHR  1.51653276 2.228752 1.733567 3.003979
#BATF::JUN_CCR9 0.07703724 0.000000 0.000000 0.000000