I don't think this is a good characterization of Mochizuki or his Inter-universal Teichmuller theory. The vast majority of new results in both pure and applied mathematics are accepted by the mathematics community without incident - this applies to extremely sophisticated and groundbreaking work as well. For example, if you look at the work of almost any Fields medalist in the last century, you'll see that it was contemporaneously well-received.

What you're citing is one example of 1) an extremely complicated proof, 2) delivered to the mathematics community in a very unorthodox manner, 3) by an author who has demonstrated significant reluctance to refine their work to make it more comprehensible to others. This is very uncommon and doesn't actually support your point (not that your point doesn't have merit, but this just isn't really applicable).

I feel your framing of Mochizuki's IUT could be interpreted as saying that he somehow developed a robust proof which is, for a variety of reasons, not accepted by the community at large. This is not the case - his proof is not robust! There is significant evidence that it doesn't actually work. Furthermore, if your attempt at a proof does not agree with the general consensus of the mathematics community, it makes more sense to conclude that your proof is likely in error than it does to use it as an example of how proofs are subjective, and different people could require different levels of rigor. That's almost never the case in real world peer review - you're more likely to have your math paper dinged for a subjective assessment of how interesting or useful it is than because the reviewer actually finds it to in error.

I'm also going to have to strongly disagree with you in regards to Euler's proofs. Analysis as a discipline is far more mature than it was in Euler's time, but Euler still clearly proved the things we attribute to him. I'm not really sure what your expectation is here - we have more sophisticated means of articulating proofs, and likewise much more mathematical scaffolding to support new theories. But Euler's work is rigorous.

> Having known many many pure mathematicians, I believe that they don't want to use computers for the simple reason that many of them don't know how to, and thus denying the legitimacy of computer-generated (or assisted) proofs protects their livelihood/careers.

Trading anecdote for anecdote: I've never known a single mathematician who felt that computer-generated proofs posed a threat to their careers. I don't mean to call your experience into question, but frankly I'm a little shocked that this is your interpretation of their reluctance to use computers. In my experience mathematicians are loathe to use computers not because they feel threatened by them, but because they just don't need to and never learned to. That's a very different attitude!

As for my own opinion: the legitimacy of computer-generated proofs and the work of professional mathematicians are independent of each other. It would be naive to think that computer-assisted proofs would actually threaten a mathematician's livelihood. From the discussions I've had with mathematicians both in person and online (such as on /r/math), I'm fairly sure most of them would consider this idea incoherent and not actually be concerned about it. In fact, most mathematicians I know (myself included) would be thrilled to have more computer-assisted proofs available.