The culture that the counterculture of the 1960's opposed was the anti-establishment culture. Their overly conservative lifestyle and beliefs is what they opposed.
Opposition to legalized abortion caused many conservatives to oppose the ERA.
cause
some groups do not want insider status as they may oppose govt all together or feel they will have to compromise their beliefs e.g ALF. however some groups are unable to gain insider groups this could be because of the methods they practice or their beliefs. governments generally do not like to be associated with controversial groups for instance groups associated with euthanasia. other groups may be unable to gain insider groups because their beliefs do not coincide with the beliefs of the government, this means that a groups status may change depending on simply who is government. so in answer to your question some groups choose outsider methods simply because of their beliefs and others may have to use outsider methods such as consulting opposition parties as they are unable to become recognised as legitimate by the government.
The America First Party which was formed in 2002 and claims to reflect the values of the American people. They are pro-life, pro-guns, and wants to end affirmative action and racial quotas. In addition, they oppose unlimited and illegal immigration.
Christians might oppose a homogeneous society, which are groups of people that have common ties with race, ethnic or religious backgrounds, because of the way they were raised and their beliefs.
Test the beliefs using scientific methods. In most cases the beliefs will turn out to be unfounded.
Socialist oppose goverment interference with the economy.
Creationist
Usually those are the cultures that oppose freedom.
Generally speaking, the Left-wing in the US tends to oppose participation in wars.
They generally oppose it.
They believe in equality of all members; make decisions by consensus; oppose prisons and war.
People's values influence their beliefs about social programs and taxation in that they either find it necessary to support the programs or oppose them
The KKK operated as a secret society and was therefore difficult to control or oppose.
Loyalist forces were adamant about maintaining ties to King George III while the Patriots were determined to oppose the King. Many Patriots ended up as enemies to the crown for their beliefs and actions.
Generally speaking, republicans oppose gun regulation.