Maybe.
The government is seeking only prospective relief, meaning that the EO is looking to end birthright citizenship for a particular class of persons moving forward. as you state.
However, when the SG was asked at oral argument whether the administration would seek to apply its order retroactively, the SG refused to say that it would not. In other words, the government did not commit that it would not look to rescind the citizenship of US citizens who were naturalized under old laws.
As Justice Sotomayor noted, the US has done this before when it rescinded citizenship for american indians. Given the cruel nature of this administration in regards to non-white immigrants, and the bipolar nature of donald trump, i dont think you can say with any certainty he would not look to deport as many brown people as his government agents could get their hands on.
And if you disagree, why dont you ask stephen miller what he thinks.