I don't know why SELinux complained but it proved that the problems were caused by am missing shared library.
Starting tarantella directly (/home/username/.tarantella/clients/i3li/5.10.907/ttatcc resulted with an error (libXdmcp.so.6 missing).
Allthough I had the 64-bit version of this library installed, I also had to install the 32-bit version. (yum install libXdmcp.i686)
It is odd that Oracle only ships a 32-bit version of this application without mentioning that one has to install aditional 32-bit library's :-(
It was that one of our system administrators said that I could download a tarantella client at http://ejdv.tce.com.tw/cgi-bininstall.cgi. Without his help I wouldn't have found this client.
It is that you gave me a link to the requirements but I still don't know how I could find this page (starting at Oracle.com)
Pointing to a bugreport (that was the only place I found where it said that I had to install additional libraries) is not something I would call as fully covering the requirements.
I may be wrong but for me the Oracle-site is still one of my least favourite sites. It is that sometimes I have to visit but I'm always frustrated and irritated.