Bostrom agrees. From Chapter 11 of his book Anthropic Bias:
I wish to suggest that insensitivity (within limits) to the choice of reference class is exactly what makes the applications [of observation selection effects] just surveyed scientifically respectable. Such robustness is one hallmark of scientific objectivity.
[...]
It pays to contrast this list of scientific applications with the various paradoxical applications that we discussed in earlier chapters. Take the Doomsday argument. In order for it to work, one has to assume that the beings who will exist in the distant future if humankind avoids going extinct soon will contain lots of observer-moments that are in the same reference class as one’s current observer-moment. If one thinks that far-future humans or human descendants will have quite different beliefs than we have, that they will be concerned with very different questions, and that their minds might even be implemented on some rather different (perhaps technologically enhanced) neural or computational structures, then requiring that the observer-moments existing under such widely differing conditions are all in the same reference class is to make a very strong assumption. The same can be said about [other paradoxes described in the book]. These arguments will fail to persuade anybody who doesn’t use the particular kind of very inclusive reference class they rely on—indeed, reflecting on these arguments may well lead a reasonable person to adopt a more narrow reference class. Because they presuppose a very special shape of the indexical parts of one’s prior credence function, they are not scientifically rigorous. At best, they work as ad hominem arguments for those people who happen to accept the appropriate sort of reference class—but we are under no rational obligation to do so.
Bostrom agrees. From Chapter 11 of his book Anthropic Bias: