I'm used to hearing works-salvationists quote Romans 6:16 in an effort to support salvation by works, but apparently, sinless perfectionists also use it in an effort to support sinless perfection.
Works-salvationists typically ignore "servants of obedience unto righteousness" in Romans 6:16 and simply stress "obedience unto righteousness" as if works of obedience which "follow saving faith in Christ" are "unto righteousness," works righteousness.
There is a contrast here between servants/slaves. There are only two kinds of servants/slaves in this world, in the spiritual sense;
servants/slaves of sin unto death, or
servants/slaves of obedience unto righteousness. When we place our faith exclusively in Jesus Christ for salvation/believe the gospel by trusting in His finished work of redemption as the all sufficient means of our salvation, we then
become "servants of obedience unto righteousness."
Being slaves of sin is put in the past tense. Paul goes on in Romans 6:18 -
"You have been set free from sin and have become slaves to righteousness."
Notice in Romans 10:10 - For with the heart one
believes unto righteousness..
Notice in Romans 4:5 - But to him who does not work but
believes on Him who justifies the ungodly,
his faith (not works) is
accounted for righteousness.