I'm not Indian, but I've been interested in the culture for a while, and my potentially-incorrect understanding is that henna/Mehndi is not in itself religious but rather a community-oriented part of a celebratory event. I think it becomes inappropriate/cultural appropriation when the cultural activity in question becomes re-fashioned by outsiders as symbolic of some other value (most often something sexual) rather than just interest/solidarity with the parent culture, and/or when it's only "acceptable" if a white/western European person does it. For example, I'm Latina, and hoop earrings are often paired in the media with "trashy" or "low class" Latinas. Yet, recently I'm seeing Bauble Bar and a bunch of other stores selling a lot of hoop earrings; I don't care, hell I'm happy to have more choices, but why is it trashy if I wear them, but not trashy if a blond wears them?
On a potentially more controversial point, I think it also has to do with how the minority group that has their cultural thing X appropriated (or potentially appropriated) is seen in the eyes of the culture in power, because that way one can tell whether the appropriation is from admiration or a mockery/condescending thing. I'm Latina, and the best stereotypes about Latinas are that they maybe work hard (as maids), cook tasty foods, and sometimes are bombshells a la Sofia Vergara. These are the preconceived notions people have about me, before we've spoken. There is no stereotype that Latinos are intelligent or capable of achieving the educational success expected of "model minorities". When some person appropriates some facet of my culture, it feels more like they are accepting the "non-shitty" part of my culture, almost in a "Wow, I'm s impressed you were able to do that", way, or that they're happy they get to "Cinco de Drinko". I feel like the appropriation of Mehndi and the like are more from a place of admiration than condescension. Of course, I'm perceiving all this from my shoes, and "benign" stereotypes and/or fetishizing are also damaging.
The unfortunate part of this entire topic is that it doesn't depend on the actions/beliefs of the parent group, but rather how it's perceived in the outside.