abordagem do KISS, com awk
awk -F, '{c = 0; for(i=1; i<=NF; i++) {c += $i == "0" ? 1 : 0}} c <= 3' file.csv
gene,v1,v2,v3,v4,v5,v6,v7
gene1,0,1,5,0,0,4,100
gene2,1,0,0,0,5,210,2
com perl
perl -F, -ne 'print unless (grep { $_ eq "0" } @F) > 3' file.csv
gene,v1,v2,v3,v4,v5,v6,v7
gene1,0,1,5,0,0,4,100
gene2,1,0,0,0,5,210,2