There may well be some "sympathisers" -- but you can't really know one way or the other. The policy we design ought to be based on finding a balance between preserving our security as far as possible while also recognising that a great deal of the people are refugees from a war-torn state. It isn't going to be easy to find such a balance but it ought to be the target.
With respect to AOG's "the majority aren't genuine refugees" claim, I wonder if this is a misinterpretation of Eurostat's data:
http://ec.europa.eu/eurostat/statistics-explained/index.php/Asylum_quarterly_report
This source explains that 213,200 non-EU asylum applications were made during April-June 2015, of which "only" 44,000 were from Syria. So I think that's about 1 in 5 (eg this article:
http://www.dailymail.co.uk/news/article-3240010/Number-refugees-arriving-Europe-soars-85-year-just-one-five-war-torn-Syria.html -- similar figures are also available from other newspapers so this isn't Daily Mail spin, just the first hit on Google). On the other hand, a great deal of the rest came from Iraq, Iran, Afghanistan, Albania, Somalia, Libya, Kosovo, Ukraine... if the criterion for being a "genuine refugee" is that they can only come from Syria then fair enough -- but there are other states that are less than stable in the world and their claims for being "genuine refugees" are just as legitimate.