Of course tarring the whole group with the same brush is sloppy thinking. But it's not inaccurate to generalise a group based on trivially establishable common features if you acknowledge that you're generalising. The overwhelming majority of teabaggers are white. The overwhelming majority are Christians. The overwhelming majority are conservatives. The overwhelming majority get their information from Fox or other conservative sources. Islamophobia is rife across the entire US, not just the tea party, as is the attendant racism.
If anything, looking at the original libertarian membership who are/were more progressive is taking the uncharacteristic extreme of the group, not the other way around. Social Conservative influences have dominated the discourse and promotion of the Tea Party since it entered the mainstream consciousness, and as a result it's not just the public perception that's changed.
But we're mixing politics with our religious discussion now. We should probably turn towards religion some time soon or I'll have to move the thread.