Referring to Why use the full .NET Framework with ASP.NET Core?, it appears .NET 4.7.2 is the way to go forward?
Our existing application targets .NET 4.6.1 using ASP.NET Boilerplate.
Is it mandatory to migrate to .NET 4.7.* in order to leverage ASP.NET Core 2.1 features?
No, it is not necessary to migrate to .NET 4.7.* in order to leverage ASP.NET Core 2.1 features.
You only need to migrate to .NET 4.7.2 if you need features in Announcing .NET Framework 4.7.2:
References: