What groups advocate and establish "unlicensed" churches in the US? In the United States, most churches file papers of incorporation and formally apply for 501(C)3 status. A few choose not to, a notable example being the Indianapolis Baptist Temple Church in Iowa whose building was seized by IRS in 2001 for a related issue. They had no Employer Identification Number, as they refused any form of government registration. Please ignore the details of the tax case as it's not related to the question. 

There are many groups historically which tried to avoid being entangled with the government in any way. What groups today advocate refusal to file these basic documents?
Most of the churches that do this do so as they are fiercely independent from any government over the local churches. As a result, they are also in denominations or groups that exercise little control over them, or they are not part of denominations at all. Many churches only even consider incorporating when they get larger (mine incorporated after being around for 30 years and with 500+ members)

As part of this, the groups that these churches are a part of also do not universally reject 501(c)3. 

Churches that might go this way are congregational in polity. So, Baptists, Brethren Churches, Bible Churches, Non-denominational, Amish, or other misc. Anabaptist.