Can a church be wrong in terms of doctrinal teaching? If they are in those area that are less fundamental, will it do them any eternal damage?
The answer should be obviously, "yes." In the letters to the seven churches in Asia in Revelation 2-3, only one didn't have anything said negative about the group. These churches were warned that they would no longer be Christ's if they did not straighten up soon. "Remember therefore from where you have fallen; repent and do the first works, or else I will come to you quickly and remove your lampstand from its place--unless you repent" (Revelation 2:5).
The problem when someone says these teachings are important and those are not so important is that it is man who is deciding what God should see as important or not. When a group is willing to go against God's teachings on matters, even on things you might consider minor, it shows a preference to put man's wants above God's. "For do I now persuade men, or God? Or do I seek to please men? For if I still pleased men, I would not be a bondservant of Christ" (Galatians 1:10). And yes, changes to God's teachings are always damaging. "I marvel that you are turning away so soon from Him who called you in the grace of Christ, to a different gospel, which is not another; but there are some who trouble you and want to pervert the gospel of Christ. But even if we, or an angel from heaven, preach any other gospel to you than what we have preached to you, let him be accursed. As we have said before, so now I say again, if anyone preaches any other gospel to you than what you have received, let him be accursed" (Galatians 1:6-9). That is why Paul warned, "For I know this, that after my departure savage wolves will come in among you, not sparing the flock. Also from among yourselves men will rise up, speaking perverse things, to draw away the disciples after themselves. Therefore watch, and remember that for three years I did not cease to warn everyone night and day with tears" (Acts 20:29-31).