You will undoubtedly run into issues when knowing a "new" way of doing things without having been brought up in the "old" way of doing things. It's unavoidable, really. I'd suggest learning the basics of WebForms code if possible, if for no other reason than to be able to trudge through it when necessary. Of course, if you find yourself in the position of having to support a WebForms application, you'll learn by doing just like anything else.
This question reminds me of my early days in .NET (which were the very early days of .NET in general) and trying to find assistance with various issues. I was an entry level developer, hitting up forums and such with questions. Everywhere I went, people weren't really adopting .NET just yet. They were all old Windows platform developers, whereas .NET was my first Windows development (I was all UNIX/Linux in school). Invariably, nearly every question I asked was answered with something suggesting that I "just use COM." Of course, I wasn't familiar with this. It was "the old way" and I was using "the new way."
It was difficult to work past that, and you'll likely face the same issue here. Basically, when people have made a career out of doing something the one single way they know how, they tend to expect everyone else to know it as well and will cling tightly to it as their bread and butter. You can be better than that, but it'll require patience :)