The Bible has plenty to say about such things as "false apostles", "false prophets", "false teachers", "false brethren", and "wolves in sheep's clothing". During his own incarnation, Jesus' main opponents were the likes of the chief priests, the Pharisees, the Sadducees, the scribes, and the lawyers (those who handled God's law), or what we might rightly call the religious establishment, so we shouldn't really be surprised if/when we encounter the same type of opposition ourselves.
When facing said opposition, we must follow Christ's example:
I Peter chapter 2
[19] For this is thankworthy, if a man for conscience toward God endure grief, suffering wrongfully.
[20] For what glory is it, if, when ye be buffeted for your faults, ye shall take it patiently? but if, when ye do well, and suffer for it, ye take it patiently, this is acceptable with God.
[21] For even hereunto were ye called: because Christ also suffered for us, leaving us an example, that ye should follow his steps:
[22] Who did no sin, neither was guile found in his mouth:
[23] Who, when he was reviled, reviled not again; when he suffered, he threatened not; but committed himself to him that judgeth righteously:
When facing opposition, especially from those who claim to be "Christians", your best bet is to simply look up and get God's assessment of the situation because he always judges righteously. If God's assessment is that the things that others are saying about you is true, then humbly repent and seek reconciliation with the offended party. If, however, God's assessment is that the things that others are saying about you is not true, then just pray for your false accusers and move on.
There are a lot of people in this world, including right here on this very website, who are much more concerned about their own reputations than they are about God or doing what is right in his eyes. In other words, they're after the praises of men instead of the praise of God.
Anyhow, the real underlying issue is always PRIDE because it is only by pride that contention comes. Just stay humble yourself, and you'll be fine in the end.