Some other ways in which these men were radical include their aggressive advocacy for the Civil War Amendments, the 13th, 14th and 15th, their desire for real land reform in the South, and their belief that the Federal government had a responsibility to pursue civil rights and equality in the social, political and economic terms of the day.
Abolition of slavery was a foregone conclusion, yes, but consider the 15th amendment, which gave black men the right to vote. Considering where slaves had been, legally, only a few months before, that was undoubtedly a radical act.
Men like Senator Thaddeus Stevens, who supported the concept of "40 acres and a mule" for each freed save family believed we should break up the southern plantations and redistribute them to former slaves, an utterly radical act.
Stevens also believed in the Conquered Province Theory, which would have permanently denied southerners their citizenship, and run conquered seceding states as though they were under martial law, as conquered provinces. While this didn't pass, nor did 40 Acres and a Mule, they are certainly radical ideas for their time.
In terms of their attitudes towards the freed slaves and towards the role of government, the Radical Republicans were pretty radical, especially when compared to Southern Democrats.
We can see this most of all in the Republicans' attempts to give rights to the freed slaves. In addition, we can see it in the fact that they pushed hard for more universal male suffrage and for more elective state offices. These were things that were pretty normal in the North, but not so much in the South.
At the same time, the Radicals were much more aggressive in having the government try to help the people. For example, they increased spending on public education and on what we might call welfare programs. Again, these were mainly radical when compared to what the Southern Democrats wanted.
So compared to the rest of the North, they were only radical in terms of their ideas on race and Reconstruction. But compared to the Southern Democrats, they were very radical.