There are a number of differences, though. Roberts isn't trying to claim that she was a cradle Hindu (Dolezal found a black man to claim to be her father, with the implication of being her birth father). Roberts isn't taking any leadership positions in Hindu organizations or trying to speak publicly as a Hindu; she's been quoted as specifically refusing to speak about religion. Other Hindus, one would assume, helped her in the process of deciding to convert. She isn't trying to claim any identity other than a person who happened to convert to Hinduism and is practicing Hinduism privately.
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.
"Roberts isn't ... trying to speak publicly as a Hindu"
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 not saying it should be a standard, and in fact I would argue that it's a completely unreasonable standard. I mentioned, positively, converts to Eastern Orthodoxy who join the clergy. (One of the best known modern writers about Eastern Orthodoxy is Kallistos Ware, a metropolitan bishop, who converted from Anglicanism at age 24. Nobody would call him second-class!)
I'm just saying that it happens to be true for Roberts, and that this differentiates her case from Dolezal's.
In plenty of cases, the outsider or convert better understands the religion than the native believer. I saw a documentary about Mount Athos, and all the young Greek monks were admitting that being a monk was just a way to get out of the everyday grind. I'm sure the non-Greeks had greater sense of purpose because they had to go further (not just geographically, but spiritually)
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.