How does scholars' denial of the possibility of NT autographs affect the Christian doctrines of biblical inerrancy and infallibility? Modern textual critics have adopted the Coherence-Based Genealogical Method as opposed to the traditional Local Text-Types Theory (reflected in the updated NA28 standard text). Along with this shift in approach to textual criticism comes a belief that it is impossible to reproduce an an "autograph" of any New Testament writing - only an "initial text" (Ausgangstext) can be constructed which is only the hypothetical reconstruction of a text that stands at the beginning of a textual tradition. How does this affect the traditional Protestant Christian beliefs in scriptural inerrancy and infallibility, particularly for those traditions that continue to use the Nestle-Aland (and future UBS) texts for scholarly study of the Greek New Testament?
It doesn't affect it at all. Inerrancy and infallibility are only attributed to the original autographs. It's not applied to translations, copies (even early ones) or modern versions. If it were applicable to translations then we'd have a bigger problem in the Wicked Bible. 

The belief that we can't reproduce an original autograph doesn't mean there was no initial autograph. And it was only the initial autograph that is inerrant, doctrinally speaking.

Along with this, the Reliability of the translations, meaning we believe they are accurate enough to be trusted as doctrinal sources, is still defensible via manuscript evidence, so there is still no problem.  

We have always accepted flaws in modern versions, and even the idea that our oldest known manuscripts are not likely perfect reproductions of the original manuscripts.  However, since we can reasonably reconstruct enough to understand the meaning, minor flaws in modern versions are inconsequential.

It's only the straw-man version of infallibility - the one that claims we think modern translations (or even old copies of the original manuscripts like the Textus Receptus) are inerrant - that is knocked down by this method of textual criticism.