The fact that you live so close to the water makes these questions very important. Let's examine the project from a system approach as all of the independent parts make up the system that will protect your home from the wind-driven rain in your area.
New-Construction versus Replacement Windows
Let's approach the system from the inside out. You mentioned that you are replacing all the windows in your home. I agree with your contractor that new construction windows -- complete with nailing fin and built in j channel (for your new siding) -- will provide superior weatherproofing. These parts are meant to work together to keep rain off the wood sheathing of your home. Using replacement windows would force the system to depend on caulked wood seams. While building code allows this, it is assumed that the homeowner will inspect and maintain the caulking/sealing in the years following the renovation. Quite simply, caulk shrinks and creates the perfect conditions for air and moisture infiltration.
The next part of your system is exterior insulation. You mentioned a foam backing for the vinyl siding; however, unless you are considering Mastic Structure the foam is actually insulation for your home. Mastic Structure is insulated siding that has tongue-and-groove foam that is installed over your house wrap. By virtue of the fact that you mentioned nails, I believe you are installing an insulation board over the plank sheathing (typical of a 1952 home in New England). This insulation board is taped to prevent air and moisture infiltration. The facing of many exterior foam boards is vapor impermeable and is the point of your question: "I wonder if the breathability issue (of the house wrap) is over-emphasized?" This question has two answers: yes, and no.
If someone were to apply house wrap to a wall without an impermeable vapor barrier installed as part of the assembly (i.e., no rigid insulation), the house wrap would allow any moisture in the wall assembly or moisture trapped behind the house wrap to escape. In most New England homes built in 1952, the house breathes both ways depending on the season. In this case, house wrap is essential.
Your renovation could include the installation of an impermeable vapor barrier if the foam board has a facing created for that purpose (most do). This facing would eradicate the ability for the house to breathe from the inside out and lead you to your conclusion that house wrap is not necessary. The short answer is that it's not. The long answer is that you need to know the specifications of the insulation product and ensure that it is installed properly (joints taped and/or ship-lapped boards) and that the wall assembly is insulated properly to avoid a conductive loop. Building Science Corporation has published a great document on managing moisture for residential wall and roof assemblies you can reference as you plan for your renovation. Figure 17 shows a wall assembly with exterior rigid insulation that may match your project. Be sure your wall insulation specifications match and you can eliminate the house wrap.
In many cases the contractor will not want to eliminate house wrap for a number of reasons. If you find yourself installing house wrap, I recommend Green Guard RainDrop or Typar House Wrap. My preference is Green Guard Rain Drop because the complementary flashing and tape products that Green Guard manufactures are top notch. However, the laboratory test scores for Typar are some of the highest in the industry.
I've used Mastic brand siding exclusively and find the product to be superior to many contractor-grade options available. That said, the fact that I've used it exclusively does create a bias, but I continue to depend on this product for a reason: it's a great product!
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You should also read Susan Davis's Ask A Pro Q&A, "Should I choose vinyl or non-vinyl replacement windows?" for more on this subject.