heh, that sums up about 99.9% of disagreements on the forums.
so, lets take it to the next level, what are you basing your word on in this case?
I should rephrase it as my "opinion" against yours.
First of all, even with all the mud-slinging from one kashrus agency to the next, it's a known thing that most kashrus agencies work with one another at the end of the day, as long as they're both orthodox. That includes both Eida and Rabbanut.
Second, I have simply never heard of an Eida embargo against being in contact or doing business with Rabbanut. I can understand the Eida not relying on Rabbanut, even if they were so bold to consider Rabbanut 100% unreliable. But not doing business with the Rabbanut is a completely different story. There is absolutely no reason for it, nor any gain. It sounds childish to me that the Eida would put Rabbanut in a so-called cherem. If, for some reason you believe that there is such an unspoken embargo, continue to the next point.
Third, when Eida is hired in an establishment in addition to Rabbanut, they are technically working with each other. They don't mind using the rabbanut mashgiach if he's reliable, and they split the payments to the mashgiach. That is already considered doing business with one another.
Fourth, the Eida is a for-profit hechsher. If they could make more money by selling stuff to the Rabbanut, they would.