In JWese, "conscience matter" is code for
We can't actually find any Scriptural support for our personal opinion. We've tried and tried, but no verse can be twisted so far without setting off the alarms of even the most retarded publishers. So, since the Bible remains totally silent on the subject (or actually supports a view diametrically opposed to ours), we'll only yell at you and publicly humiliate you, rather than throw you out.
As the real gods of JWs, the "Society" have taken it upon themselves to make up doctrine. Contrary to Scripture, not only do they rely on their own understandings, but they demand you rely on it too. Also, contrary to Scripture, not only do they feel perfectly qualified to direct their own steps, but demand to direct yours too. In addition, contrary to Scripture, you are ordered to put your faith in earthling man, in whom there is no salvation. But since there are still non-JWs left to be converted and a few JWs with functioning brain cells, they couch their self-idolatrous and blasphemous demands in noble-sounding double talk. Any JW who's ever been dragged into the back room knows, what the words say in the Watchtower and what they are intended to be interpreted as, may be totally opposite. When an article makes it very clear that a tattoo, beard, music, etc. are left to our consciences, what they really mean is
Now that we've told you what the Society God feels, you're supposed to voluntarily adopt our God's feelings. If you don't, you obviously lack a Watchtower- Bible-trained conscience and your mentally-diseased and demonic decision is trumped by our positions apointed by the Watchtower corporation Holy Spirit.