A minority of converts might embrace radical interpretations of Islam, but radicalism is much more common in this group than in the average Muslim population.
Conversion to Islam among native Europeans is on the rise. Many converts live at peace within their native societies; some convert only for marriage, and reject neither contemporary culture nor Europe's Judeo-Christian values. A minority, however, embraces radical interpretations of Islam and can pose a security risk. The involvement of Muslim converts in recent terrorist attacks has raised concern in Europe about these "converts to terrorism." While intelligence agencies and security services track international communications and guard borders, such homegrown terrorists pose just as potent a threat to the security of Western democracies. European security services and politicians remain unprepared to handle this growing phenomenon.
Source: Middle East Quarterly (English)
See also: Islam, liberal democracy, and converts