Should governments tolerate the actions of dissent groups?What does this issue involve and why is it important? What underlying values must i...

The key word in your question is "should".  So you are
asking us to make a moral judgement about the value of dissent in society and whether a
government should put up with it.

Should they? 
Absolutely.  One of the foundations of democratic government, what makes it functional,
is compromise.  That is, compromise between opposing ideas and elements of government. 
What dissent does is offer (hopefully) constructive criticism of government policies and
actions.  If there is enough dissent and it is directed in the right places, it can
improve government and society.  Government reacts to it, because in the end, it is
accountable to the public.

If you want to be more objective
still, simply compare the countries and governments that do and don't tolerate dissent. 
Do: The US, Japan, Britain, Germany, France.  Don't: Iran, Pakistan, Myanmar,
Cuba.

Which list would you like your government to belong
to?