This will probably lead to lowering taxes to an acceptable (for almost everybody) level.
Why do you think that? They would increase the taxes instead.
Actually, I'll tell you what happens when masses don't want to pay taxes... The people that pay taxes get rich, and the rest begin working for them. Sounds counter-intuitive, doesn't it?
First, they increase barriers of entry to do anything substantial. Sure, you can sell trinkets online or baby sit, but that will be the limit of your business reach. Business that conform dominate every market and pass the expenses to the customers. Customers rush to gray markets, but they also get overwhelmed by big businesses in time.
Moral of the story: You need to have a very good plan if you are going to challenge the State's power.
Now, back to the topic, you are still saying this:
You don't have to be a libertarian to use Bitcoin.
No, but you cannot be against libertarianism either, you have to accept that there are libertarians (and even anarchists & crypto-anarchists) using the currency and live with it.
Otherwise sooner or later you will start to fight what you don't like, which makes you an enemy of Bitcoin - that is what I am talking about.
This is speculation on your part. What if I don't think it will ever come to that because libertarians are impotent? I can perfectly support Bitcoin because of some features I like, and I might think that the potential use by libertarians will never be a problem in a scale greater than the benefit Bitcoin brings.
You could say that they might become damaging to your plans of using Bitcoin to libertarian ends, but that's what being an enemy of libertarianism means anyway.
I don't know if classical liberalism and libertarianism is the same, though. 
