Avalonia does not currently support updating classes via a setter, but you should be able to fully control the colors of the progress bar without using classes. When you say "colors are set as a style", I assume you are referring to the semantic color variants like accent, danger, success, and warning. In the case of CircularProgressBar, these variants are simply used by the default control theme to change the IndicatorBrush property, as shown in the snippet below:
<!-- accent -->
<Style Selector="^.accent">
<Setter Property="IndicatorBrush" Value="{actipro:ThemeResource ControlBackgroundBrushSolidAccent}" />
</Style>
<!-- danger -->
<Style Selector="^.danger">
<Setter Property="IndicatorBrush" Value="{actipro:ThemeResource ControlBackgroundBrushSolidDanger}" />
</Style>
<!-- success -->
<Style Selector="^.success">
<Setter Property="IndicatorBrush" Value="{actipro:ThemeResource ControlBackgroundBrushSolidSuccess}" />
</Style>
<!-- warning -->
<Style Selector="^.warning">
<Setter Property="IndicatorBrush" Value="{actipro:ThemeResource ControlBackgroundBrushSolidWarning}" />
</Style>
Here the IndicatorBrush property is updated to one of our predefine theme resources that correspond to the semantic color variant. In your scenario, you could update the IndicatorBrush property directly based on the value thresholds you define.
