I believe technically you can. But they will make it as inconvenient as possible. As someone who travels for work, I’ve accepted it as a necessary evil.

Legally you can opt out but that won't stop then from telling you you can't and refusing entry without it regardless.

Can't speak for other countries but in the US you are allowed to opt out (for now)

tldr: you can opt out, but it doesn't matter.

At this point in history, opting out of a single face scan at the airport is sort of like walking on the beach for a mile and making a point of walking back to two specific footprints and wiping them away.

Between the ubiquitous phones pinging your phone every few feet or capturing your image, airplane cameras, the hundreds of cameras throughout the airport, thousands throughout the city on lampposts, in the buses you took, your taxis or rideshares, supermarkets, gas stations, bodegas and everywhere else, in the vast majority of countries your identity is being captured and tracked constantly.

That's just where technology is at in the vast majority of countries at this point in history. I live outside of city centers, I use cash and don't use rideshare apps, but I book plane tickets, I pass through city centers, I use ATMs to withdraw that cash, and 10 years ago in Vietnamese mountain villages I bikepacked to days away from the nearest town, where every building was a hand-built bamboo shack, every villager(about 30 people) had at least one smartphone.

A Viet family from that village who invited me to spend the night in their shack had a couple smartphones per person, bluetooth karaoke microphones(that was super fun), two smart TVs and an Xbox with a kinect(or whatever the new iteration was). Full internet access and electricity, and they lived in otherwise full undeveloped jungle a kilometer away from the 30-people village along a single road that experienced a mudslide a month previous that had no timeline for being cleared. We all recorded our dinner and karaoke together, they posted and streamed it on facebook or wherever real-time and afterwards.

Living in parts of entirely disconnected rural Afghanistan or other yet-recovered war-ravaged countries is still an option for "privacy-focused" individuals, but in about 15 years I doubt even the rural towns in those countries will be entirely excepted from blanket identity tracking.

Cameras and ID software are already affordable and become moreso literally each passing day, and the advantages to law enforcement and data brokers are already beneficial and become moreso literally each passing day.

This ironically does not eliminate privacy altogether, I believe in the "there's so much going on and being recorded nohody is going to care if I'm smoking a joint in an alley with a camera" future. Before cameras, we were tracked by our immediate communities. In the middle camera age a decade ago(before ubiquitous digitization), it felt invasive, and now we're past that and living in nascent transmetropolitan where everything and everyone is recorded and analyzed all the time to the point that soon nobody is going to look at you unless you are literally consecutively Jack the Ripping in plain view.

I don't like being tracked, but it isn't exactly a battle I have any say in and there are historical privacy policies being developed now that will shape how the future looks. If citizen rights are robust, tracking doesn't functionally matter much more than your elderly neighbor eyeing you from the porch.

Now in the US, identity tracking is already everywhere and citizen rights have been nearly entirely eroded, so I prefer to live abroad where I at least have much more robust functional rights as a traveler.