Even if trans-race were a reasonable thing (and the reasons that it's unreasonable are far too complicated to get into, and far too off-topic), Dolezal's actions and Roberts' actions would still be very different. Even if you lived in a world where trans-race were somehow legitimate, I'd imagine lots of people would still be uncomfortable about Dolezal's approach to it. But religious conversion, in general, has long been accepted, and Roberts' conversion is extremely normal as conversions go.
It is true that occasionally religious identities that have ethnic identities get complicated; as a random example, the Eastern Orthodox churches in the US have some trouble with this, since the communities overlap heavily with ethnic (Greek, Russian, etc.) identity, and there are occasionally some awkward spots when converts to Orthodoxy start gaining leadership roles in the church (which is reasonable!) and then trying to mold it into the vision of the church that they were looking for before their conversion. But I wouldn't doubt the seriousness of these converts' conversions, even so, and regardless, Julia Roberts is doing nothing of the sort.
I'm not sure this sounds like a reasonable standard to join any religion. "If you're a convert, shut up". Sounds like second class status. This stuff is too complicated for me.
I'm just saying that it happens to be true for Roberts, and that this differentiates her case from Dolezal's.
The situation in Iran is complicated. Zoroastrianism is a protected group there, but it's extremely dangerous to be seen as welcoming converts in the Islamic republic. Simultaneously, to convert away is basically to accede a small amount of political power. I've heard (especially in Religion in Iran[2]) that there may be a Zoroastrian movement taking shape; as converts, those folks would certainly be welcoming of converts, but it's likely to make the established group anxious because if it gains too much attention it will lead to persecution of all Zoroastrians in Iran. So you have two overlapping marginal groups each trying to exaggerate the figures in opposite directions—which is sort of thematic for the kind of contradictions you see in Iran generally.
[1]: http://www.huffingtonpost.ca/byblackscom/rachel-dolezal-is-n...
[2]: https://www.amazon.com/Religions-Iran-Prehistory-Richard-Fol...
On the other hand, 'cultural' Jews are more likely to marry non-Jews, and absorb them into Judaism that way. And I suppose this leads to cultural Jews leaving Judaism too. I think I read somewhere that the descendants of all the founders of Reform Judaism ended up outside Judaism.
That doesn't follow; converts are very often quite passionate about the beliefs of the group they convert to, and it's distinction form others, but that doesn't mean that they necessarily prefer the version that is seen as most pure by outsiders.
http://www.npr.org/sections/parallels/2015/10/10/445343896/i...
You can convert to Judaism, but you can only be born a Jew.
i.e. The difference between a religion and an association with a culture.