If a Republican wanted to work for a Democrat, and if he were denied employment for that reason alone, that would be illegal, yes.

I don't know where you're getting this idea from, but you really should check your sources.

There is a limited prohibition against screening for political affiliations enforced by the Federal government when filling certain civil service positions, but that's about it.

For a good summary of what types of discrimination can and cannot trigger legal liability, see here:

http://www.eeoc.gov/facts/qanda.html