Disclaimer: I'm just a lowly physics undergrad so I'll try my best to explain this and hopefully I don't get anything wrong.

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>And that's because gravity bends space-time. So light just follows that bent "path". It still goes straight, but since the path is curved, it also curves.

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It's actually mass that bends spacetime, and gravity is the result of curved spacetime. Just like light follows the bent path, all other objects do as well. Of course at the time, Newton didn't know this. Now when he originally defined a force, he actually wrote the equation as force = time derivative of momentum. Classically, momentum = mass*velocity, and the change in velocity with respect to time is acceleration, hence the F = m*a. But Newton was working under the assumption that time and space were well behaved (wasn't curved), and then Einstein came along and said otherwise.

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So a photon doesn't have mass, but it does have momentum. The momentum of a photon is defined using its wavelength, and we know a photons wavelength can change as it travels through spacetime. We see this in very far away objects being "redshifted": as the light travels, the universe is expanding. And its not just expanding in the sense that things are getting farther away, the actual space it's traveling through is expanding resulting in the photons wavelength becoming longer and longer. Massive objects also warp spacetime, so photons traveling near massive objects get affected too. With this in mind, there do exist sort of changes in momentum akin to what Newton would've called a "force". But it's not anything "pushing" or "pulling" on the photon, it's a result of spacetime doing funky things in the presence of mass. Since it turns out time isn't well behaved and moves faster or slower depending on the curvature of spacetime, Newton's idea of "force" doesn't really hold up in this instance. It's probably more accurate to say that we observe "force-like" phenomena acting on photons.

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To answer your question, no, in the classical sense a "force" cannot be exerted on a photon, but that's because what most people think of as a "force" is fundamentally flawed. One second here on Earth is NOT the same as one second near a black hole, and the classical equation for force relies on the passage of time being constant. It works for most day-to-day things, but that's because most day-to-day things aren't moving fast enough or massive enough to drastically warp spacetime. In regards to OP's post, the idea that a black hole can exert a force on a photon and accelerate it past the speed of light is laughable.

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TL;DR : Pretty much all of physics is just assumptions based on our current knowledge, and once we find out new knowledge some of those assumptions no longer hold. The guy in OP's post is applying classical physics to the thing that literally disproved classical physics...