Imagine, if you will, an individual who attends services at two church's on two separate days of the week. Faithfully. Maybe a Wednesday Sunday split, or a Saturday Sunday. This individual can meet the provided 'definition' of an involved, committed, submissive 'church member'. And, they can obtain this bar of achievement for both locations. Or, imagine a teaching Elder, who creates deep relationships at his full time congregation within his local church, but also at his weekly bible study he hosts at his home or at work.
When a committed member of a church who has multiple deep relationships with other members moves away - those relationships don't have to end. As Paul traveled, his commitments and dedications didn't with prior locations.
I'm not saying that these individuals would need to hold membership at multiple church's - i'm just saying with our current constructs of membership, this type of situation is rather difficult.
When Paul was planting churches- i.e. local congregations- there weren't multiple denominations. There was one. And those congregations were under the leadership, ultimately, of the Apostles who planted them; who sent others to plant churches; who convened in councils to settle doctrinal disputes. Paul was not a minister of a local congregation: he was an Apostle, charged with a specific duty. One cannot compare his role to that of a minister or elder in a congregation today.
Today, however, we do have denominations. You seem to ignore this reality and operate on the basis that each church is an isolated assembly and one should be able to go to the one on Sabbath which offers the best Sabbath worship experience and then go to the one down the road on Wednesday because it has a better Bible study. This is not how it is meant to be.
Ideally there would be only one "denomination" as there was in the days of the early church, and there would be a congregation in each locality or parish and there would be unity (and of course uniformity) across the board. But because of declension (and sin) there has been split after split in the body of Christ. Some separations were required and Biblical and others weren't. It is the duty of the Christian to find and align himself to the most Biblical congregation
and denomination he can (I don't agree with joining a particular congregation because it happens to be good on certain things when the denomination it is a part of is in error. That's independency and therefore unBiblical).
When one joins a particular congregation and denomination one is making a commitment to that denomination's witness and stand; he is throwing his lot in with them; he is saying that this denomination's position is the most Biblical and the purest witness to the Christian faith. To then attend meetings in other denominations is to contradict that stand and to suggest that the separation which exists between these two bodies isn't that significant after all. It undermines the witness of the denomination of which he is a member. This is why I would guess that some in your home church are critical of you going elsewhere.
Denominations are an unfortunate necessity in this world but one should also act as if there were only one church and so commit to one body which he believes provides the strongest Biblical witness.
Taking this line, it is perfectly fine for a member in one congregation to attend services in another congregation of the same denomination. Indeed this should be encouraged, for example if one's denomination holds communion seasons or if one is on holiday, or studying away from home. In the case of the latter, a student studying away from home should seek out a congregation in his own denomination to attend whilst away. If that is not possible then, if there were a church which was close to his own, perhaps it would be ok to attend there although he should certainly seek guidance from his session. If the only churches in his area are liberal/false churches then he would be better not attending anywhere and worshipping alone at home and listening to sermons. But then maybe he shouldn't go to study in an area where there aren't any churches he could attend.
I think being on holiday is a slightly different matter. One is only away for a short period of time. If there isn't a congregation of one's own denomination then I think it acceptable to attend the most Biblical church one can find, or staying at home on Sabbath if there aren't any (clearly, since one is only on holiday for a short time, one shouldn't feel that he can only go on holiday to a place where one of his own congregations is located). Although I can also see the argument for not attending any congregations in churches outwith one's own denomination, even when on holiday. If, after all, one believe's one's own denomination has the purest witness then perhaps he shouldn't go elsewhere at all. I wouldn't hold to that myself but I think there's a lot to it. I, personally, think the command to worship in the public assembly on Sabbath gives me warrant to attend another denomination's worship if I'm away from home for a short period. I'm making no commitment to that church; I wouldn't partake in Communion in that church. I think if one is working away from home for a significant period or studying for four years and is attending a particular church, one is making a commitment to it and is more involved in it and therefore the situation becomes more complicated.
None of this prohibits friendships with Christians in other denominations or having fellowship with Christians in other denominations, on a personal level. But one must be careful that his conduct, on an institutional level, doesn't undermine his own denomination's witness which is, after all, his witness. If we are separate from others there must be a reason, otherwise it's merely schism which is a sin. And if that reason doesn't prevent you attending other denominations on a regular basis, or even partaking in the Lord's Supper in other denominations- the closest form of fellowship one can have within the church- then I'm not sure why the separation exists. I don't think it's enough to say one church is "better" than another. It's not about that. It's about the witness of the church and the denomination and if you don't think the separation prohibits you from regularly attending other churches- especially those in your own locality- then you're effectively saying you or your denomination is schismatic.
This all assumes, of course, one is meant to be a member in only one congregation. But going back to the early church I think that's clearly the pattern. A believer is meant to be a member in a local congregation of the church. He is not meant to travel around like a tourist; he is not meant to travel great distances (unless he absolutely must because, for one thing, that would be breaking the Sabbath to travel unnecessarily). When Paul commands that Christians are not to neglect the assembling of themselves together it is in regard to the assembling of the local congregation; not in the abstract.
