While I'm terrible at predicting the future, I find this hard to believe. I think screening your DNA is something maybe upper/middle class parents might do. I do not believe it is being done by those that cannot afford it.
https://www.nhs.uk/conditions/genetic-and-genomic-testing/
As the cost of doing it comes down, i would expect it to be offered more widely. I don't know if it will ever be cheap enough to offer to all prospective parents.
Oddly, the cost of doing genetic tests does not scale at all linearly:
https://www.rbht.nhs.uk/sites/nhs/files/Laboratories/CGGL%20...
(eg a single arrhythmia test is £650 - £900, but the whole panel is £1000, and then it's only another £150 to do multiple panels)
Meanwhile, sequencing a whole genome is ~$1000:
https://www.genome.gov/about-genomics/fact-sheets/DNA-Sequen...
Perhaps a lot of the cost is sample preparation, and the actual molecular genetics bit is dirt cheap.
After birth a blood test is used for scanning for 25 rare known issues.
https://www.rigshospitalet.dk/undersoegelse-og-behandling/fi... -> in Danish.
This is the same for everyone.
Of course, this is exactly the point of Gattaca: you won't be "forced" to do it, but you and your child will be punished for making the socially unacceptable "choice".
It won't be long before it's dirt cheap and standard in most countries, especially as the Affymetrix/Illumina patents expire and the genechips get commoditized.