I personally think that FRs would be screaming their heads off at the site of foreign troops on our soil...even the IDF.
They're "on our soil" all the time anyway--in case you didn't know, we train military from many countries, including some from Israel. As long as they're here anyway, they might as well roll up their sleeves and pitch in. (And for the record, we, too, deploy spies in some instances--and if we don't, we should.)
The US military regularly trains with troops from several nations on our soil. They have been doing so for years. Not all of those troops are from NATO member countries either.