What I get from that letter is this:
''If you live in a country where you will be persecuted for not voting, you may go to the voting booths, just dont put in a ballot (if the booth is private), or do not mark your ballot with anything that would be choosing a political party.''
It's an arrangement so that the rank and file brothers and sisters can have a clear conscience about going to the voting booths (while not voting) in countries where they may be persecuted for not voting.
I dont read anywhere in the letter that voting itself is a conscience matter, as it is stressed that christians must remain neutral. they are refering to christians making an ''appearance'' of voting.