The history of my denomination is littered with people who pretended to be one thing to influence the affairs of congregations they were not loyal to. Back before the Brotherhood Restructure of the 1960's Disciples of Christ, we were one fellowship with what became the Independent Christian churches. Some congregations believed in cooperative enterprises and participated in them; others were opposed to them. People loyal to the non-cooperative congregations would join membership in cooperative congregations, get a measure passed withdrawing from cooperative enterprises -- and then promptly leave that congregation to do the same to another.
Attendance does not mean loyalty. These people were not attending non-cooperative congregations, but their loyalty was to non-cooperative congregations. Regardless of where they were, they had committed their loyalty to non-cooperative congregations. They had absolutely no business pretending to be part of the cooperative portion of the brotherhood.
I know that you are splitting hairs trying to justify something, namely continuing to present yourself Baptist even when you are committed to a non-Baptist congregation.
It ought to be evident to any reader that no amount of sophistry can make that okay.
If I was to attend my Disciples of Christ congregation, but decide that I want to call myself Baptist, and write to the nearest Baptist church and ask for membership privileges to be extended to me while I stayed at my congregation, would I be out of line? Yes I would. The Baptist congregation hopefully would expect me to attend their congregation regularly, then they would consider whether or not I could be a member and have membership privileges.
If I was to actually follow that directive, and go to the Baptist congregation regularly for home congregation, I would no longer be entitled to claim to be a Disciple of Christ. This would especially be the case if I was to place membership at the Baptist congregation. If I was to turn around, decide to go to the seminary in Indianapolis and register as a Disciple of Christ to get reduced tuition, while attending a Baptist congregation as a member, I would be in serious trouble. I would not be a Disciple, but a Baptist.
If a person is attending a non-Baptist congregation for home congregation, s/he has no business claiming to be Baptist here.