You don't want the single quotes to get propagated to the makefile. Don't quote them, and replace them with double quotes - that would keep the variable value as one word in the shell.

make -f make_gene_read_count.mk -n SAMPLES_OUT="$SAMPLES_out"

You don't want the single quotes to get propagated to the makefile. Don't quote them, and replace them with double quotes - that would keep the variable value as one word in the shell.

make -f make_gene_read_count.mk -n SAMPLES_OUT="$SAMPLES_out"

If you want to pass more variables, separate them by unquoted whitespace:

make VAR1="some value containing $val" VAR2='some other value'
#                                     ^