You can do this pretty easily in python, you'll read through File 1 and save the 7th column in a list. Then read through File 2, delimit the 5th column on the slash ("/") and if the element before the slash is in your list then print the line. Example code would be:

inFile1 = open('file1','r')
inFile2 = open('file2','r')
printList = []

for line in inFile1:
    lineList = line.rstrip().split('\t') #Generate a list split on the tab
    printList.append(lineList[6])  #Append your tag to printList

header = inFile2.readline()  #Remove header
print(header.rstrip())

for line in inFile2:
    lineList = line.rstrip().split('\t') #Generate a list split on the tab
    (tag,junk) = lineList[4].split('/') #Split your tag on the slash
    if tag in printList:
        print(line.rstrip())

Personally, I'd recommend doing this in awk since you can get through it with just one line of code:

awk 'BEGIN{OFS="\t";FS="\t"} NR==FNR{tagArray[$7];next} NR>FNR{split($5,ARRAY,"/"); if (ARRAY[1] in tagArray) print $0}' file1 file2

This uses tabs as delimiters (BEGIN{OFS="\t";FS="\t}) then it reads in the first file and saves the 7th column in an array called tagArray (NR==FNR{tagArray[$7];next}). After it starts reading in the second file, it splits the 4th column on the slash, and if the first element of the 5th column is in tagArray is prints the line (NR>FNR{split($4,ARRAY,"/"); if (ARRAY[1] in tagArray) print $0}).