awk + grep solution:

awk '/^[^0-9]/{ 
         m = ""; cmd = sprintf("grep -m1 %s file2", $0);
         cmd | getline m; close(cmd);
         if (m) next; 
     }1' file1

• cmd - crucial grep command
• m - variable filled with possible matched item

The output:

1
GACGGAGGATGCAAGTGTTATCCGGAATCACTGGGCGTAAAGTTTTTTTTT
2
3
4
GACGGAGGATGCAAGTGTTATCCGGAATCACTGGGCCGTCCGTAG

awk + grep solution:

awk '/^[^>0-9]/{ 
         m = ""; cmd = sprintf("grep -m1 %s file2", $0);
         cmd | getline m; close(cmd);
         if (m) next; 
     }1' file1

• cmd - crucial grep command
• m - variable filled with possible matched item

The output:

1
GACGGAGGATGCAAGTGTTATCCGGAATCACTGGGCGTAAAGTTTTTTTTT
2
3
4
GACGGAGGATGCAAGTGTTATCCGGAATCACTGGGCCGTCCGTAG