Using bash for loops in conjunction with embedded applescript for bash scripts

There are a few issues with your script: some that stop it from working entirely; some that get it to do the wrong thing; and some that needn't have been there in the first place. There are couple of other answers that address some points, but neither of them appeared to test the script because there's a lot they don't address.

...for each host found in the hosts2.txt file... 
...Each host is listed on its own line.

Then this line:

for HOST in `cat ~/bin/hosts2.txt`

is not what you want. That will create an array out of individual words, not lines in the file. You want to use the read command, that reads a file line-by-line. You can structure a loop in this manner:

while read -r HOST; do
    .
    .
    .
done < ~/bin/hosts2.txt

As @entraz has already pointed out, your use of single quotes will stop shell variables from being expanding within your osascript.

Then there is the AppleScript itself.

I'm unclear why you included a repeat loop.

The purpose of the script is to open a new terminal tab on my Mac and automatically launch "screen -r $HOST" in each new terminal until the end of the list of hosts in the hosts2.txt document. Each host is listed on its own line. It is repeating 2 times because there are only 2 hosts listed in the text document

This makes no sense, given that you implemented a bash loop in order to read the lines into the $HOST variable. Granted, you were reading words, not lines, but the AppleScript repeat is a head-scratcher. Bin it.

Then you have this:

tell application "Terminal" activate
tell application "System Events" to keystroke "t" using [command down]
tell application "Terminal" to activate

That's approximately infinity times the number you need to tell Terminal to activate.

This line:

set host to $HOST

will throw an error for two reasons: firstly, host is taken as an existing name of a property in AppleScript's standard additions, so you can't go and set it to a new value; secondly, there are no quotes around $HOST, so it's not going to be recognised as a string. But, this is just for your learning, as we're actually going to get rid of that line completely.

Finally:

tell application "Terminal"
    do shell script "screen -r " & host in front window
end tell

is wrong. do shell script is not a Terminal command. It's a command belonging to AppleScript's standard additions. Therefore, if the rest of your code worked, and it got to this command, Terminalwould execute nothing. Instead, the shell scripts would run in the background without an actual shell, so that's not much good to you.

The command you're after is do script.

Sadly, it does appear that, in High Sierra at least, the AppleScript commands to make new tabs and windows in Terminal no longer work, so I can see why you resorted to System Events to create a tab in the way that you have. Thankfully, that's not necessary, and nor are your multiple activatecommands: do script will automatically run Terminal and execute a script in a new tab by default.

Therefore, the only AppleScript command you need is this:

tell application "Terminal" to do script "screen -r $HOST"

The Final Script

Putting this all together, here is the final hybrid script:

while read -r HOST; do
    echo "$HOST"
    osascript -e "tell application \"Terminal\" to do script \"screen -r $HOST\""
done < ~/bin/hosts2.txt

Alternatively

If you wanted to take the loop from bash and put it in AppleScript instead, you can do so like this, for which I'll use a heredoc (<<) to simplify the use of quotes and aid readability:

osascript <<OSA
    property home : system attribute "HOME"
    property file : POSIX file (home & "/bin/hosts2.txt")

    set hosts to read my file using delimiter {return, linefeed}

    repeat with host in hosts
        tell application "Terminal" to do script ("screen -r " & host)
    end repeat
OSA