This is one of the many reasons I left the church of Christ denomination: too many legalists and too many rules. The biggest reason was that the local church I went to, endorsed both the Iraq and Afghanistan wars. Wow. So yeah, I've heard all these arguments and have found flaws in all of them. This is how they are taught to evangelize and they don't care if they break the rules to do it. It's deceptive and that's really sad. The Gospel should never be cloaked in deception.
Here's the thing, churches of Christ are autonomous, meaning there there is no synod. So, there's no body certifying which church is legit or not. Ergo, any church can claim to be a church of Christ and in fact, most of them do. In reality, every Christian church is by default a church of Christ. Of course, that doesn't stop many church of Christers to claim a monopoly on the truth and salvation. They are trying to keep everybody else out of heaven, which reminds me of a certain discourse between Jesus and the legalists of his day...
Matthew 23:13 “Woe to you, teachers of the law and Pharisees, you hypocrites! You shut the door of the kingdom of heaven in people’s faces. You yourselves do not enter, nor will you let those enter who are trying to.
15 “Woe to you, teachers of the law and Pharisees, you hypocrites! You travel over land and sea to win a single convert, and when you have succeeded, you make them twice as much a child of hell as you are. -NIV
See how these Pharisees were doing the very same thing and Jesus condemned them for it? You don't get to pick and choose who gets into heaven. That's Jesus' job, and he says you better be all about the love, or you're not getting in. You're not a disciple if you don't love. No, being self righteous doesn't cut it. Saying the right things isn't enough. It doesn't even matter if you aren't a member of any church. Just love. Put the needs of others over your own needs. Minister to the sick, the widows and the elderly. Let your example, not your arguments win people over to Christianity.