The program I'm interested in is COMPHEP. I have ubuntu and it wants redhat. If I try and download and run it anyway is there a risk that I will damage my system some how?
You should find a source tarball for COMPHEP and you could compile that (perhaps asking help on the COMPHEP forum).
In practice, if you download a binary, it won't break your system if you try running it. However, it could crash, and you'll better run it first in some terminal to notice that.
In theory, a malicious developer could make some executable which detects the distribution and do bad things on your system. Since you are a theoretician, read about the halting problem (perhaps also Gödel, Escher, Bach) then about trusted computing bases and ken thompson's compiler hack. So when you download some program, you need some trust (more a social issue than a technical one in practice).
Ubuntu are based on Debian, so it uses Debian packages, so the .DEB package will run better than .RPM.
But if you really want to use the red hat version (RPM), just download the rpm and convert it using alien. I think the worst that can happen to you, is that the program will just not run.
If it is a production server dont install any packages DEB, RPM, tar.gz without testing them first in a identical test computer.