This is going to sound a bit like a rant and may really need to be edited, but you're going to get the full-force of what I have to say. Even if that includes a few errors in spelling and grammar.
The big word you see as the post title is a term from contract law. It also appears in general legislation. From a legal perspective, as far as I understand (though you might check with Howell Scott) what this word means is this: some agreements and laws are setup that if part A is deemed bad, part B still applies.
An example would be when Congress passes a Frankenstein law, one that has merged unrelated issues, they add a "severability" clause. That way, just because the extra paycheck for Congress gets ruled unconstitutional, the extra taxes can still stay. Or a contract will have a clause that is deemed illegal, but the rest of the contract stays in force. You could make the future interest payments on a mortgage illegal, but the severability means you still owe the principal.
I think it's time we draw the principle of severability into American Christian life. (Note: there is a decent gap between pure Biblical Christianity and Christianity as expressed in American culture. We'll deal with that another day.) It's time for us to assert the need (and the right) to sever certain things in theology.
One of the big debates in Baptist life right now is connected to the theology of salvation. The issue is over how much of a free-will mankind has in their salvation and how much is God's sovereign election. The catch-phrases are "Calvinism" and "Arminianism."
Calvinism strongly stresses God's sovereign election while not denying man's responsibility to respond. Arminianism strongly stresses man's freedom to respond while acknowledging God's omnipotence (All-powerfulness). The terms come from two theologians from about 5 centuries ago, Calvin and Arminius.
When this argument comes up, usually someone that is strongly against Calvinism will jump from the issue to the parts of Calvin's theology that are no good. (Like burning heretics, merging church and state, for Baptists, infant Baptism.) Calvinists will highlight the tendency in Arminius to ignore eternal security and leanings toward legalism. (Or antinomianism, depending…)
There are more modern examples: there have been good advocates of homeschooling, discipleship, and church renewal. Some of them have then said other really dumb things: there's one who wrote a book showing support for slavery in the American South, several who are way too far in the "fathers are the heads of households" direction (guess what? I'm ok with my wife being responsible for some stuff all on her own. I think it's Biblical as well.)
Then there are those who have evolved their beliefs over time. At one point, a professor at New Orleans Seminary was a staunch proponent of Biblical Inerrancy (the belief that the Bible contains no errors). Now, he leans towards open theism (the belief that sometimes God doesn't know stuff). You've got some of the various doofuses (doofi? is that the proper plural for doofus?) with TV shows and TV networks. They have moments they are right. Then they have extended epochs of dumb.
It's time to acknowledge that there's some severability here:
Time to separate that just because someone's been right once doesn't guarantee they're right now.
Time to separate that just because one idea was good does not mean the next one is.
Time to separate that just because an individual has a TV show he's not a true spokesperson.
However, we can't expect those who attack Christianity to allow this if we don't do it. If we Christians continue to be circle-the-wagons fanboys for our celebrities, we will always be subject to these problems.
We have to be more discerning. We have to continue to re-evaluate and return to Scripture for our answers. We cannot keep giving a free pass to the people we like and hope that they always get it right.
We also need to be willing to give credit where it's due: the idea may be good even if the source is bad. Grab and use the good. Hold on to the good, discard the bad.
And when you're evaluating people: don't assume one blog post makes them an expert. Or that liking one blog post or reading one book is a lifetime endorsement. I like Tolkien's writings: that doesn't make me a Catholic. I like JC Ryle. I'm not Anglican. There's some Presbyterians I like, but I pastor a congregational church and don't intend to change it.
In all, weigh it, consider it---but be willing to sever the bad and discard it.