$ while read id1 id2; do
   printf '^%s[[:blank:]]+' "$id1"
   printf '[^[:blank:]]+[[:blank:]]+'
   printf '[^[:blank:]]+[[:blank:]]+'
   printf '[^[:blank:]]+[[:blank:]]+'
   printf '%s[[:blank:]]n' "$id2"
done < f1.txt > regexp.txt

$ egrep -f regexp.txt f2.txt

$ while read id1 id2; do
   printf '^%s[[:blank:]]+' "$id1"
   printf '[^[:blank:]]+[[:blank:]]+'
   printf '[^[:blank:]]+[[:blank:]]+'
   printf '[^[:blank:]]+[[:blank:]]+'
   printf '%s[[:blank:]]n' "$id2"
done < f1.txt > regexp.txt
$ egrep -f regexp.txt f2.txt

id1 id2
id1 id2
id3 id4
id3 id5
id4 id5
id4 id6

id1 TYHYU 61728497 rtyheyia id2 8372819203948
id1 UJLJF 57383930 utkjruak id2 5683903048377
id1 UJLJF 57383930 utkjruak id2 5683903048377
id3 THREE 4444444 adfhdd id4 182i3746
id2 NOPE 4444444 adfhdd id4 182i3746
id3 TREEE 555555 affff id5 8435987345
id4 FOUR  555055 asdfl id5 3728462
id4 FORE  6666666 dfiuyd id6 845687234

^id1[[:blank:]]+[^[:blank:]]+[[:blank:]]+[^[:blank:]]+[[:blank:]]+[^[:blank:]]+[[:blank:]]+id2[[:blank:]]
^id1[[:blank:]]+[^[:blank:]]+[[:blank:]]+[^[:blank:]]+[[:blank:]]+[^[:blank:]]+[[:blank:]]+id2[[:blank:]]
^id3[[:blank:]]+[^[:blank:]]+[[:blank:]]+[^[:blank:]]+[[:blank:]]+[^[:blank:]]+[[:blank:]]+id4[[:blank:]]
^id3[[:blank:]]+[^[:blank:]]+[[:blank:]]+[^[:blank:]]+[[:blank:]]+[^[:blank:]]+[[:blank:]]+id5[[:blank:]]
^id4[[:blank:]]+[^[:blank:]]+[[:blank:]]+[^[:blank:]]+[[:blank:]]+[^[:blank:]]+[[:blank:]]+id5[[:blank:]]
^id4[[:blank:]]+[^[:blank:]]+[[:blank:]]+[^[:blank:]]+[[:blank:]]+[^[:blank:]]+[[:blank:]]+id6[[:blank:]]

$ egrep -f regexp.txt f2.txt
id1 TYHYU 61728497 rtyheyia id2 8372819203948
id1 UJLJF 57383930 utkjruak id2 5683903048377
id1 UJLJF 57383930 utkjruak id2 5683903048377
id3 THREE 4444444 adfhdd id4 182i3746
id3 TREEE 555555 affff id5 8435987345
id4 FOUR  555055 asdfl id5 3728462
id4 FORE  6666666 dfiuyd id6 845687234