I don't know where you live, but I'm a member of a Coptic Community in a place that has a lot of Catholic and Protestant churches, and one EO (Greek) church. I've only lived here for about 10 months, but people in our community tell me that before we were assigned our current priests (from the nearest Coptic Churches, one state over) and hence were able to start having services about 16 years ago, the few Copts who were here did
go to the Greek church, and were communed there with full knowledge of both the Coptic diocesan bishop and the EO priests and bishop. This stopped, of course, once we were sent Coptic priests, but we still have particularly good relations with the Greeks here. We also seem to attract a few of the Catholics (uniate) people who are of Middle Eastern background, as apparently not all of them are satisfied with the Arabic-language Eastern Catholic liturgies that are held semi-regularly at the local Byzantine Catholic church, so they come to us even though our liturgy is 75-80% English. Go figure.
We have not had such a rush to Protestant services, thank God, but then our priests and also our laity provide a good and relatively constant message regarding our doctrinal stances, which makes it clear why we cannot attend such services. At least one of our members unfortunately did so anyway at least once (he was dating a woman who is "non-denominational" or some such), and rather than being sucked into that life, he came back to report to us how terrible it is and how we should never
do as he did, even once!
So I think a lot of it can be handled by redoubling our commitment to Orthodoxy, no? At least that is my experience. Maybe it is harder in bigger communities or actual churches (we are about 40 people total).
Back home in Northern California, the OO are all Habesha (Ethiopians and Eritreans), but they commune at the local EO (OCA and Bulgarian) churches, because there is no OO church of any kind for many, many miles. They are fully integrated, so I don't suppose that there is much of a problem with being given the cold shoulder as there might be in other EO parishes. Perhaps this is even why they don't yet have their own church (while they do have their own restaurants, etc.), but I don't know. I attended the OCA church that some of them attend and was also given a very warm welcome despite being at that time still RC, so I can understand their attraction to that particular community, though I do pray that they get their own church soon (not because I am upset at OO receiving at EO churches, but because until communion is restored I would rather an OO church be established, as I have been told in no uncertain terms that I as a Coptic Orthodox Christian that I am to not receive in the OCA church under any circumstances; I guess not all jurisdictions or all places are equally permissive).