Herd immunity for measles requires a vaccination rate of 95%.
Attaching a moniker "quack" at will is no way to have a discussion.
But the author goes far beyond that conclusion and rails against the very idea of herd immunity, and claims that since herd immunity may not be possible in practice when dealing with measles, there should be no stigma against opting out of vaccination. These conclusions are very weakly argued, and the obvious counter-arguments are not addressed.
Sebastian Funk, Associate Professor at the Centre for the Mathematical Modelling of Infectious Diseases at the London School of Hygiene & Tropical Medicine: "to achieve [termination of measles transmission,] the population immune needs to be 93-95%, the herd immunity threshold." (https://www.who.int/immunization/sage/meetings/2017/october/...)
There is a substitution of terms in the first statement that you quoted. To stop transmission you need 90-95% of the population being _immune_ to the disease, not vaccinated against it. Do you see the difference?
The second quote by Funk got it right. But again please read the article why this is unattainable even with the 100% vaccination rate.