Suppose there are two friends: one holds of the eiruv and the other doesn't. Is the second allowed to ask the first to carry for him?
And if the first anyways carried it, can the second benefit from it?
There are different reasons why some people do not use Eruv's.
If you do not use it since you hold that it is no good, then you would have no right to ask someone else to carry for you, as you are according to your belief causing him to be Mechalel Shabbos. However if you hold that really it is good, however you do not use it in order to remember there is such a Halacha as Hotzaa on Shabbos or for whatever other reason, then there is no problem asking someone else to carry for you.
As always CYLOR