In article , Gary
Harnagel writes:

"Inflation isn't falsifiable, it's falsified -- BICEP did a wonderful
service by bringing all the Inflationists out of their shell, and
giving them a black eye." - Roger Penrose

Despite his substantial contributions, Penrose is now an outsider.

So the inflationists voted on physics?

I'm not sure what you mean here. Of course, science is not a democracy;
the majority can be wrong. However, there is a consensus that
inflation probably happened and that Penrose is probably wrong on this
point. In any case, there is debate, and the issue is not solved by
quoting arguments from only one side (especially the minority).

"Even from the beginning, inflation looked like a kluge to me-- I rapidly
formed the opinion that these guys were just making it up as they went
along" -- Neil Turok

Turok has his own axe to grind, with Steinhardt. Check it out. Do you
think that it is more believable?

Sure they have their own ax to grind. So did Lemaitre. So does Hawking.

The point is that the quote makes it sound like they have some
independent evidence against inflation, whereas in fact they are touting
their own alternative theory. As for Lemaitre, he had a hypothesis
which went beyond what was known at the time; it was not a rival to
another hypothesis attempting to explain the same thing.

Is there anything to the claim made at the end of "Theory of Everything"
that Hawking is now trying to refute that time had a beginning?

Whether or not time had a beginning does not alter the fact that we can
trace the evolution of the universe back to a time when it was very hot
and very dense. By convention, the time at which it had infinite
density according to a naive extrapolation (which no-one believes
accurately describes the very early universe) is known as the big bang.

And it's funny that mathematics with singularities is used
to validate predictions, no?

No, because they are not used to validate predictions in the regime with
singularities. I can navigate fine with latitude and longitude as long
as I am not at the north or south pole.