No true Scotsmen. Sorry, but you don't get to define for others what a Christian is. Out there somewhere there is a more fundamental one that says you're not a real Christian either... and so on.
And Jews would say no Christians are correct followers of the Judeo god. Same as Muslims would say. And vice versa. And yet, categorically, nearly everyone that is an absolutist believer is wrong, because everyone can't be right, but all will still believe they are. Their .1% of the population is the right one. Must be nice to be so right.
Hey, to each their own. If a loving god doesn't allow mistakes in understanding for the fallable humans it created (which I don't believe) then 99.999999% of us are screwed to begin with and the rest is moot. It would mean salvation basically comes down to luck (belief is almost completely correlated with where and when you were born).
You're kind of undermining the desire of the "Christians have an ugly history here" argument by then allowing anyone to identify as Christian, and assigning such a degree of relativity to Christian beliefs. Hell, the argument started that Christians are hypocrites (don't live up to their beliefs) and has morphed into "who can really say what they believe?".
There are some pretty basic beliefs that traditional Christian doctrine has defined as central and definitive. People can disagree. People can even disagree and call themselves Christians. That's between them and God. But it's completely legitimate for core Christianity to have the right to define what beliefs should be associated with them, especially if we're in a bigoted discussion seeking to broad-brush the conversation with statements like "and we all know the ugly history Christianity has in this country".
At the end of the day, Christianity claims that we are all sinful, fallen humans who will never in this life be anything but sinful and fallen. We all desperately need the gospel of grace that states that Jesus died for our sins, took the condemnation for that and gave us His rightstanding before God because God loves us and that's the only way we could be saved.
It goes on to say that of we prioritize fruits of the Spirit over the lusts of the flesh, then the power of the Spirit can change our character, but the reality is taught that we will always carry those lusts and at any given moment, we are susceptible to failures of character. We have a constant war within us, and we are guaranteed to lose battles.
So, we will continue to live that tension.
The Christain Bible, the core canon of scripture for our faith, says that Jesus Christ (For whom the faith is named), spent a LOT of His time teaching what the church would be like after He died and went to be with the Father. A HUGE swath of that included goats and tares--i.e. people who would claim to be a part of the faith but who would not be.
So, have genuine Christians done reprehensible things both before and after coming to the faith? Yah. Are we hypocrites? Yah. The core belief predicted we all would be and states, as a matter of fact, that that's why its gospel is so important.
Can we look at everything done by anyone claiming to be a Christian and attribute it with broad brush to "Christianity"? No.
And it's surprising, in this modern, enlightened, tolerant culture that hates bigoty and stereotypes, that this is still a discussion people want to try to pawn off as legitimate.
Maybe a better, more fair discussion would be to go through the canon of Christian scriptures, discuss what they say, and then discuss what it means to individuals. That seems like a much more interesting conversation. I'm up for it. How about you?