The same way random things like coffee and salvia get banned.
The first group of people to upload were the ultra wealthy.
Their status re: legal death was unclear which led to countless lawsuits from the extended families of those individuals.
To help build public support there was an extensive PR campaign by the heirs to smear the uploaded. After all it's easier to have someone stripped of legal personhood if they're already wildly unpopular with the voters.
They appealed to the religious by declaring the uploaded as soulless abominations against gods law.
They appealed to the soccer moms with rumors of the uploaded inhabiting depraved hedonistic simulations.
They appealed to the Luddites convincing them that copies of the uploaded would take their jobs.
Popular TV shows had plotlines revolving around sex offenders fleeing justice by means of uploading.
Murder mysteries liberally use the concept of an uploaded villain pulling the strings of a murder.
Which all sets the stage for the final nail in the coffin.
Fleeing war criminals
Some time later somewhere in the world a war is fought against genocidal essentially-Nazis. As the coalition troops close in on the bunker rather than taking cyanide pills the entire upper echelons of the regime upload themselves escaping.
In the following wave of outrage the concepts associated with uploading become synonymous with the essentially-Nazis.
Governments ,already resentful of having to deal with individuals who can move country between one clock cycle and the next and faced with voters who think upload is just a way for nazis, pedophiles and murderers to escape justice, take advantage of the growing public sentiment to push through countless anti-upload laws.