It's not the Act of 1871 which subverted the constitution. It was "An Act providing a permanent form or government for the District of Columbia" of 1878 which did that. I've attached a pdf. I highlighted the section which supercedes the constitution for the District of Columbia.
That said, you opt into that jurisdiction by certifying that you are a "US person". "US" is the District of Columbia and all territories under exclusive control of the federal government.
http://www.supremelaw.org/fedzone11/htm/chapter4.htm
A "person" is the corporate personhood laid out in most Acts of congress.
The lawyers screwed the people slowly - not overnight with one Act.