One criticism I often hear from the nationalistic cradle Orthodox people is that we American Orthodox are too watered down with "Protestant influence" or "Protestant theology" seeping its way into the Church. I see a similar attitude coming from American Protestant converts to Orthodoxy who go through great lengths to try to abandon their previous faith affiliation by criticizing virtually anything that resembles it, going so far as to condemn coffee-hour as "Protestant innovation" or sermons in the middle of the Liturgy (common in the OCA) as bad.
My questions and thoughts are this: does it really matter? The Church has ALWAYS incorporated elements from native religions and/or cultures into its worship and theology. We stole monogamy from the pagan Romans even though the monotheist Jews were polygamous, the Church Fathers practically built our theology upon Greek philosophy taken from pagans--see St. Justin the Philosopher--many of our "New Calendar" holidays fall exactly on or at a very close date to ancient pagan holidays, etc. Heck, the Russians even have Western Choirs and Synods, and the Greeks have Western pews.
Why does it somehow become "bad" and "wrong" when it comes to Americanism and thus American Protestantism? I see Phyletism peaking its ugly head once again. It's okay for the Greeks and Slavs to incorporate their heathen pre-Christian cultures and faiths into their Orthodoxy but it's not okay for the American Orthodox to do the same?
Honestly, you're being a bit too general here and in the process (perhaps inadvertently):
1.) Erecting strawmen (Coffee hour? Have you met Hyperdox Herman's older, meaner brother in real life or something?)
2.) Conflating "Americanism" with "Protestantism" and the theologically neutral with the theologically pregnant
Theologically neutral American cultural customs are readily incorporated into a great many American Orthodox parishes: pot-lucks, clambakes, flea-markets, raffles. The same is true with some theologically neutral customs which may be associated with (or even have their origins in) American Catholicism and Protestantism: Bible Study, Vacation Church School, the various attempts at establishing Orthodox parochial schools, et cetera.
This is different than actually "incorporating Protestantism", i.e. educational materials, forms of worship, et cetera, pregnant with Protestant theology (which you put in quotes for some reason) into the life of the Church. Asking what's wrong with doing that would be like asking "What's wrong with incorporating Arianism into Orthodoxy?". What is Protestantism? It is by definition heterodoxy. Or as Belloc defines it:
...a crop of heresies, but not one heresy; and its characteristic was that all its heresies attained and prolonged a common savour: that which we call "Protestantism" today.
It teaches in opposition to Orthodoxy, so it cannot be incorporated into Orthodoxy without compromising Orthodoxy. I don't think one would have to be an Eastern phyletist or a hyperdox convert to object to "incorporating Catholicism" into Orthodoxy in the form of sacred heart iconography or other things pregnant with Catholic theology. The same holds true for Protestantism. To contend that coffee hour constitutes "incorporating Protestantism" into Orthodoxy is ridiculous. But it is equally ridiculous to ask "What's wrong with incorporating Protestantism - which by its very definition means a deviation from Orthodoxy - into Orthodoxy?".