As [M. kanté][1] pointed out, it's open whether or not graph isomorphism is FPT when parameterized by tree-width. Furthermore, I don't believe there is any complexity-theoretic barrier to creating an FPT algorithm in this case.

For a survey of what's known about the fixed-parameter tractability of graph isomorphism, see the introduction of my paper with Anuj Dawar and Eryk Kopczyński [here][2]. In the paper we show graph isomorphism is FPT in the tree-*depth* of a graph, which is a necessary (but not sufficient) condition for graph isomorphism to be FPT in tree-width.


  [1]: https://cstheory.stackexchange.com/a/19701
  [2]: https://doi.org/10.1007/978-3-642-33293-7_21 "Bouland, A., Dawar, A., Kopczyński, E. (2012). On Tractable Parameterizations of Graph Isomorphism. In: Thilikos, D.M., Woeginger, G.J. (eds) Parameterized and Exact Computation. IPEC 2012. Lecture Notes in Computer Science, vol 7535. Springer, Berlin, Heidelberg."