Actually, it's a matter of manuscripts, so it's entirely possible that those who contain it are correct and those that don't are incorrect.
That aside, the Bible still doesn't say "Christians should snake handle." It doesn't even say, "Christians should take up snakes." Nor does it say "Christians should drink poison."
It says specifically, "they will pick up serpents with their hands; and if they drink any deadly poison, it will not hurt them."
That is akin to saying, "They will get sick and will get better."
In other words, it would not be an instruction to go make yourself sick. It is, instead, an assertion that there would be awe inspiring healings.
Now, can ANYONE out there think of an awe-inspiring occasion in the New Testament in which someone was bit by a snake and was unharmed?
Therefore, there is nothing WRONG with those texts that include this Markan passage. The problem, of course, is idiots who can't read and think.