I think the only way to do it is to move out of Austin and start converting.
Election results alone bear out the fact that Austin is still one of the few Democratic strongholds in Texas: http://en.wikipedia.org/wiki/Politics_of_Texas#Current_situa...
Did you read the rest of that paragraph? The cities tend to vote Democratic in state elections whereas the rural areas overwhelmingly vote Republican, and Texas has a lot of rural space. I'll also point out that the largest city in the U.S. to elect an openly gay mayor (reelected twice) is Houston, which I found entertaining because of the two Democratic candidates, she was the more 'conservative'. Austin isn't as 'weird' as it thinks it is.
I have never lived in any of the other major cities in Texas, so I certainly don't understand the full dynamics of their politics. I do understand that at the heart of the major cities they tend to be more liberal, which is expected of just about any major city. However, as an Austinite I can say it feels like the liberal bleeds more into the suburbs here than in the other major cities. This may be because of Austin's relatively small size or just bad anecdotal evidence. Take that as you will and I hope I didn't rustle too many jimmies.