Free trade, in the truest meaning of the term, requires zero tariffs and zero state subsidies. This would be anathema to the EU - which can fairly be called a protectionist bloc - but less so to the USA or a post (real) Brexit UK.
You seem rather confused about what Brexit is - it is the UK leaving the EU, nothing more nothing less.
We were never asked did we want zero tariffs, zero state subsidies and so on. There are all issues separate from what we were asked to vote on.