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
Harav Shlomo Zalman Auerbach paskens Meor HaShabbat (Peninei HaMoer 3:8 in regards to opening up bottle caps, which some are makpid not to open on shabbos, if one may open it for someone else who is makpid not open them says it depends on whether the one who abstains from opening it is refraining because they hold that it is inherently forbidden according to halacha, if yes than it is forbidden, however if the person is doing it only as a chumra-stringency or because it is the minhag of his father or rebbe than it is perfectly permissible to open the bottle cap for them. Thus in this instance, if the one not carrying is refraining because of a minhag and not a stringency, it is permitted.