Does a 15% across the board income tax cut (keep in mind that the top tax rates were 39.6%, if Dole's cuts were implemented it would've been the lowest rates on the top class since the 1920's) sound "moderate" to you?
The tax rates from 1993 - 2001 were 15%, 28%, 31%, 36%, and 39.6%.
A 15% tax cut would've reduced those to about 13%, 24%, 26.4%, 31%, and 34%.
The highest tax rate in the 1920s was 25%.
Dole's tax cut was fairly similar to Bush's tax cuts(10%, 15%, 25%, 28%, 33%, 35%), not very radical, but concerning to deficit hawks who had worked hard to reduced it from $290 billion in 1992(at the time, a record) to "only" $107 billion in '96.
As said before, Dole was conservative but willing to compromise. That's why he was considered a moderate.