Currently the template argument are different:
  InterfaceRequest<mojom::FooInterface>
  InterfaceRequest<mojom::blink::FooInterface>

We would have to make it something like:
InterfaceRequest<mojom::FooInterfaceBase> (or InterfaceRequest<mojom::GenericFooInterface>)

We could hide this base type with:
using FooRequest = InterfaceRequest<mojom::FooInterfaceBase>

But I am not quite sure whether the gain justify the confusion it may cause.

Maybe we could have a conversion helper:

template <class U, class V>
InterfaceRequest<U> Convert(InterfaceRequest<V>);  // a static member of InterfaceRequest

We can check that U and V are both derived classes of the some InterfaceBase, so it is still safe.
WDYT? Thanks!

Oh, maybe it is more convenient to add constructor/assignment operator for the conversion, instead of using a static Convert() function.

Yeah I was assuming that aliasing to FooInterfaceBase would be an acceptable solution.

It's more complicated than I thought though, because A) there are lots of explicit references to mojo::InterfaceRequest<SomeType> already and those would have to change  B) there are legitimate reasons for developers to want to refer to mojo::InterfaceRequest<T>. We could do some particularly evil things to allow this to work seamlessly, but let's not.

I like your idea of a move ctor+operator that enforces U::Base==V::Base

I need a solution that would not require including both variants in the same file.

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We should add a generic interface placeholder type to mojom shared headers.