First, academic freedom as it is commonly understood does not refer to one's views and publicly stated opinions, but to the freedom in which they conduct teaching in the classroom. The reference in US is the 1940 Statement of Principles on Academic Freedom and Tenure stating that
Teachers are entitled to freedom in the classroom in discussing their subject
But as a rule, academics do not get special treatment outside of the classroom with regards to freedom of speech. It's certainly not the case in the US, and I am not aware of any other country where it might be the case.
Now, regarding the impact of unpopular or offensive views on reputation, it will heavily depend on your colleagues! I personally find that, while freedom of speech is highly valued in academic circles in general, Academia as a system is a rather conservative institution and I suspect you would not find much more sympathy for extreme views than in any other workplace.
NB: Academic freedom is also used to refer to a US jurisprudence applying to universities and colleges; in that sense, it is unrelated to rights and duties of an individual teacher.