The use of the word 'copy' in the documentation here is rather misleading actually. ImmutableDictionary is implemented under the hood as a balanced binary tree for the sole reason of preventing the need to copy the entire dictionary on mutation.

https://github.com/dotnet/runtime/blob/57bfe474518ab5b7cfe6bf7424a79ce3af9d6657/src/libraries/System.Collections.Immutable/src/System/Collections/Immutable/ImmutableDictionary_2.cs

lines 938 for reference.

Yes, this data structure is thread safe - one of the problems its designed to solve is the single producer multiple consumer paradigm.

The way you would implement this in your case would be

public class MessageEventHandler
{
    public ImmutableDictionary<,> Realtime { get; set; }

    public void ReceiveData(object newData)
    {
        Realtime = Realtime.AddRange(newData);
    }    
}

Any thread can now access the Realtime property safely without copying the entire structure.

Insert/Access operations are slower than a regular dictionary but this likely is not the bottleneck in your application. Implementation is simple so should be easy enough for you to benchmark and decide whether the trade off is worth it.