One of my main concerns leading up to term and labour was having to fight off internals if I went over the 'clocked' time once in the FBC. For me it was about the cascade - do the internal, possibly see something that would officially worry the staff because of hospy policy and pressure me into something else I didn't want to do. I was also keen to have my privacy preserved as much as possible, not believing that it was necessary to have intrusive inspections to get my baby out - and that good midwives don't need to 'look' to know what's going on, using body language and verbal cues to know where you're at (which they did, in the end, as we discussed after the birth) That and wanting my belief that uninterrupted labour and birth to be absolutely respected - with my self-preparation teaching me that interruptions like internals can prolong labour and interrupt natural, mammalian processes if everything else is going normally, otherwise. As for internals outside of labour, I saw no clinical reason for these to occur and wanted to be left well enough alone, which was totally supported by the FBC staff, anyway. These were my reasons and these are the ones I'd give if someone were to ask me about internals and their merits.
If someone were to mention they wanted an internal, I would certainly ask why they wanted it and discuss it with them - not write it off without explanation or rolleyes at the caregiver (not until I'd heard the reasoning, and it turned out to be that caregiver's professional, unquestioned habit to do internals!).
So, yes, ask these same people why they object - they may give you another perspective from the ones given here