If you get put on a project like that, it's probably best career wise to find a new role.
It may be a months-long transition, even, but often if you are persistent there's nothing impossible about this, and it doesn't have to be something that you're constantly stressing about. It's just a light touch applied every so often. Once you're in such a position it'll usually be some years before you need to worry about this again. But even so, keep sticking your head up every so often and see what's going on, just to be sure.
But do it on purpose. Don't just sit back and take whatever gets assigned to you. This doesn't even have to be stressful necessarily, because while you may encounter local resistance, at the corporate level nobody is ever going to complain that you're trying to align yourself harder with where the company is going. It's not like you're asking to pursue a pet project on the company dime with no prospect of payout... it's the opposite of that in almost every way.
My portion of the work was described as “pressing a button” so I removed myself from the project at the earliest opportunity.