One of Bertrand Russell's reasons to not be a "Christian" is his understanding that the first cause argument for God's existence fails. Russell writes:
"Perhaps the simplest and easiest to understand is the argument of the First Cause. (It is maintained that everything we see in this world has a cause, and as you go back in the chain of causes further and further you must come to a First Cause, and to that First Cause you give the name of God.) That argument, I suppose, does not carry very much weight nowadays, because, in the first place, cause is not quite what it used to be. The philosophers and the men of science have got going on cause, and it has not anything like the vitality it used to have; but, apart from that, you can see that the argument that there must be a First Cause is one that cannot have any validity."
First, Aquinas's first cause argument distinguishes between causality in fieri and causality in esse. Russell speaks to the first kind of causality and not the second, which is the Thomistic first-cause argument that is stronger. So I don't think Russell here does anything that should lead anyone to not be a Christian.
Russell then says that the fallacy of the First Cause argument is that the question "Who made me?" cannot be answered because one will then ask the question "Who made the God who made me?" "If everything must have a cause, then cause must have a cause." But this is not clear. Russell was unfamiliar with the more powerful Kalam version of the cosmological argument. That argument states that everything that begins to exist has a cause. So, if God did not begin to exist, then it's clear that God will be best understood as not having a cause.
Russell writes: "There is no reason why the world could not have come into being without a cause; nor, on the other hand, is there any reason why it should not have always existed. There is no reason to suppose that the world had a beginning at all. The idea that things must have a beginning is really due to the poverty of our imagination. Therefore, perhaps, I need not waste any more time upon the argument about the First Cause."
All of this reasoning of Russell's is questionable. Our universe did begin to exist. Big-bang cosmology verifies this. Our universe has an age, and anything that has an age has a birthday. So that is one reason "to suppose that the world had a beginning at all." Further, the Kalam argument does not argue that all things must have a beginning. But it seems true that whatever does have a beginning ("begins to exist") is best understood as having a cause (therefore things that begin to exist do not pop into existence uncaused).
From this I conclude Russell has not yet given one good reason as to why he should choose to not be a Christian. I think one should never decide to not be a Christian for the reasons Russell has so far given.