It appears to me that their beliefs are no more radical than Calvinists and Calvinists were able get control/influence governments. Was waiting until someone chose to be baptized that extreme?
There were a couple of reasons. The first is that, as you say, they believe that people should be baptised as adults rather than as soon as they were born. This felt like a huge risk for those who believe that an unbaptised person could end up in hell. Many children died before the age of 2. Many never made it to adulthood. So this ideas was risking sending all those children (who would never make it into adult hood) to hell was shocking. If you were not baptised before you died your sins were not washed away and your soul was at risk.
The second, and probably main reason, was the Münster rebellion. This was an attempt by radical Anabaptists to establish a communal sectarian government in the German city of Münster – then under the large Prince-Bishopric of Münster in the Holy Roman Empire. In 1532 they attempt to force Münster to be ruled under their theological control. They took the town over and forced adult citizens, Catholic and Protestant to rebaptise. there was an orgy of iconoclasm in cathedrals and monasteries, and rebaptism became compulsory.
A proclamation was issued that all property was to be held in common.
The city was then attacked by the expelled Bishop and went into a year long siege.
John of Leiden, who was a Dutch Anabaptist leader who moved to Münster in 1533, became an influential prophet, turned the city into a millenarian Anabaptist theocracy, and proclaimed himself King of New Jerusalem in September 1534. His authority grew, until eventually he proclaimed himself to be the successor of David and adopted royal regalia, honors, and absolute power in the new "Zion".
There were at least three times as many women of marriageable age as men now in the town and he made polygamy compulsory and he himself took sixteen wives. (John is said to have beheaded Elisabeth Wandscherer in the marketplace for refusing to marry him; this act might have been falsely attributed to him after his death.) Meanwhile, most of the residents of Münster were starving as a result of the year-long siege.
Once the siege was over the anabaptist were tortured and killed.
After that their reputation lay in taters. Never again would they ever gain political power or any respectability from the other Protestant groups.