Just because someone is centrist doesn't mean they don't know what to think. It usually means they have a nuanced position on an issue that doesn't conveniently fit into a box that is red or blue.
Sometimes I'm not sure they actually can't be labelled, and sometimes the difficulty in labelling them comes from an overall lack of coherency rather than a truly uncategorisable position, but, I don't know anyone who calls themselves a centrist and could talk about politics in any depth. Centrism seems mostly, at least where I live, to be what people call themselves when they just support the status quo and wish politics would go away.
I would definitively not call myself a centrist, nor left or right. There is some good goals even in the far left and far right, but also a lot of things I strongly disagree with to the point of alienation. Centrism simply just an other political agenda with its own set of prioritized demographics and intentions.
"I will not make any deals with you. I've resigned. I will not be pushed, filed, stamped, indexed, briefed, debriefed or numbered. My life is my own."
~ Number 6
On the I-P and the way you've framed it, there centrist-on-this-question positions that don’t meet that description, e.g.:
“both Israel and various entities on the Palestinian side have engage in, and continue to engage in, actions which are intolerable and not excused by abuses on the other side The international community should cease aid to all offending parties so long as that continues, while engaging in dialogue aimed to a more complete resolution, with readiness to commit substantial resources to support a peaceful resolution.