Whether you use the singular "is" or the pluaral "are" depends on whether or not the subject number (in your case, "one") is singular or plural.
It's worth noting that because you used the number "one," you would use "is" every time. This results in some examples not being sensical. "About one" and "As many as one" sound funny because the phrasology presumes more than one, but only one is used. The listener is forced to presume that you can have partial people (e.g., one-half), but we know that can't be true, so it sounds funny. If you were talking about something that could be cut into pieces, like apples, then the two phrase forms would make more sense.
One in twenty-five people is a sociopath.
Five in twenty-five people are sociopaths.
As many as five in twenty-five people are sociopaths.
As much as one in twenty-five apples are worm-free.1
About five in twenty-five people are sociopaths.
About one in twienty-five apples are worm-free.2
1 When talking about apples, it sounds better to my ear to use much instead of many. This might be due to the expectation that partial apples are involved (e.g., one-half, two and one-quarter, etc.). I'd have to think about exactly why I feel this way, though.
2 I expect there will be an argument about this example. To my ear it sounds right, the example being plural because the subject number could be more than one. However, when you consider rules like the verb taking the plural form due to the second or "closer" element in an "or" grouping (one or two are..., two or one is...), it suggests my example should use the singular. A professional would need to chime in on this one.