The Christian and non-Christians divorce rates are the same.
Maybe nominally true, but it's lower among Christians who regularly attend church. I kinda hate using church attendance as a barometer for which Christians are real or not, but it may be the best metric we have.
When I look at scripture, what I don't see is the Lord giving the Believer permission to remarry after a divorce.
I don't know. It's possible to look at 1 Corinthians 7:15-16 (which you posted below)'s permission to count yourself as lawfully divorced as permission to remarry. One could argue, though, that even when we go with Paul's version, a condition is that the spouse who left is an unbeliever. Perhaps, and I mean "perhaps", the unbeliever distinction is how Paul's version of being lawfully divorced (which I would take as permission to marry someone else) seems to contradict Jesus' version of it being a sin to marry a divorced woman. Perhaps Jesus implied divorce among believers means unlawful to remarry (unless there was adultery).
At least, that's how I reconcile Jesus' and Paul's teachings as not being against each other, since I count them both as inerrant Scripture. If I'm right, and this perhaps is a bit too legalistic, then it's sin to divorce and remarry unless there's adultery involved and/or unless the spouse doing the divorce is an unbeliever.
I quoted scripture in which I don't see any allowance for a divorced person to remarry. Some might argue that remarriage could be inferred. What I see as common between Jesus' and Paul's teaching is not that divorce is never allowed but that allowance for remarriage after divorce is not articulated in scripture.
A problem w/in Christianity is that Believers pick and choose scriptures to follow and ignore the rest. You mention the term 'legalistic'. Are there absolutes in Christian doctrine or is everything open to negation through grace and personal interpretation?
I'm not a judge. Divorced and remarried Christians persons answer to the Lord.
Maybe a better question to ask is: "Are preachers preaching the Word regarding divorce and remarriage or are they compromising to not offend and lose congregants?" For too many, I believe it's the latter.