Unable to create a polymorphic type because the trait cannot be made into an object

The error comes from the fact that you can't create trait objects for DnsRecordData due to the trait not being "object-safe". This concept is explained in the trait objects section of The Rust Programming Language.

In your particular case, the trait contains a generic method. To create a trait object, the compiler has to synthesize a vtable for the trait, containing a function pointer for every method the trait has. But because the trait has a generic method, it effectively has as many methods as the method could be instantiated with, which is potentially infinite. Therefore, you cannot make a trait object for DnsRecordData.

The intention is that DnsRecord should be able to hold any struct implementing the DnsRecordData trait

That's not what the code says.

Vec<DnsRecord<dyn DnsRecordData>>

This is a vector of the struct DnsRecord containing the trait DnsRecordData. If you want "any struct implementing the DnsRecordData trait", you need a generic:

pub struct DnsPacket<D>
where
    D: DnsRecordData,
{
    pub answers: Vec<DnsRecord<D>>,
}

Traits can be implemented, but they also have their own type. In order to create this type, the trait needs to be object-safe - Trait Object is not Object-safe error.

As the error message states, this trait cannot be a trait object because there are generic types on the method.

The first error states that DnsRecord requires that whatever type it is parameterized with must implement DnsRecordData. However, the type of the trait object doesn't actually implement that. Normally, you'd use a trait object via a reference (&dyn DnsRecordData) or a box (Box<dyn DnsRecordData>), both of which should implement the trait, preventing this error.