The difference is that the limits on observing relativistic effects in 1905 were technological, whereas in QM you cannot observe the effects of entanglement in

The difference is that the limits on observing relativistic effects in 1905 were technological, whereas in QM you cannot observe the effects of entanglement in a non-isolated system even in principle. This is a fundamental constraint imposed by the theory itself. You can't get around it even with arbitrarily advanced technology.