Was Witherspoon orthodox in his beliefs, or was he a radical? I have heard that he was.
Witherspoon was the president of what became Princeton back when it was a strictly conservative institution, and the moderator of the First General Assembly of the Presbyterian Church in the USA.
The only thing I can think of on which he might be considered something other than orthodox was the revision of the Westminster Confession, made under his leadership, to say that the civil government should support Christianity but is not required to endorse a particular denomination of Christians.
There are a few small denominations in America which still affirm the original unamended Westminster Confession, but virtually all modern American Presbyterians have accepted the church-state revisions of the Westminster Standards.
Here is a historical essay I wrote on a related subject which includes extensive citations of the history of the confessional revisions: http://baylyblog.com/blog/2013/04/what-two-kingdoms-theology-and-why-does-it-matter
Depending on what gauge you used to define “radical”, he probably was to some.
Remember he was a signer of the Declaration of Independence and an advanced tutor to James Madison. By signing the Declaration he was immediately on the hit list of King George.
Here is a biography that on the surface deals with some of what you asked about him.
http://archive.org/stream/johnwitherspoon00woodgoog/johnwitherspoon00woodgoog_djvu.txt
“The question was not one of ortho-
doxy versus heresy but of authority versus lib-
erty ; of tyranny acting under cover of the law,
too often arbitrarily enacted, interpreted and
enforced on the one side ; and of popular rights,
as yet accepting the established church, making
no attempt to abolish it but claiming justice
and freedom within it, on the other side. This
was the condition of affairs in the church of
Scotland in the first half of the eighteenth cen-
tury. “
—
I am a great admirer of James Madison and credit some of his education to the influence of Witherspoon.