learning experience
Much of the feedback so far weighs in on the side of "required -- family is family". Someone cited honoring one's parents (the source of the request), and a couple people mentioned protecting a life (the sibling is apparently in real danger of injury without someone there).
I, on the other hand, am leaning toward "forbidden", though "permitted" is a possibility. Definitely not "required", though.
The issue is complex. While the sibling needs a caregiver, that's a service that can be hired -- so there's no apparent need for the poster to do it personally. Of course it's important to honor one's parents (this comes up a lot in text), but the talmud also teaches that if a parent asks you to transgress the Torah, you must decline (Bava Metzia 32a). This raises the question of whether attending another religion's worship service -- on its second-holiest day, to boot -- is avodah zara, forbidden worship. Is it enough if you don't intend to worship? What if you don't participate? What if you don't listen? That is a complex question with varied answers depending on circumstances, ranging from exactly what will take place to the strength of your own Jewish education and commitment, and you really need to ask your rabbi for a personal ruling.
I think the experience of facing this issue is valuable for the conversion candidate, actually. As a member of a minority religion (that sometimes faces hostility from others), sometimes you are going to have to make choices between your religion and your family/friends/society -- things like this, or resolving Shabbat issues with your employer, or various other matters. Finding out how you will handle those choices before it's "too late" -- before you convert and acquire new obligations -- seems useful to me.
I assume that most conversion candidates face some sort of religion-vs-world-at-large test during the process, but I don't actually know.

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If you're not taking PART in the service, I don't see any harm in it. I was just at the christening of a friend's child. I sat respectfully, didn't sing along with them (although that was REALLY tempting), and was there for my friends.
But I also think an awful lot of the restrictions we place on ourselves are silly.
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I've been to Christian weddings and funerals since I became religious, but not to regular masses. I think it's probably easier when you're there for a lifecycle event; people assume you're there for the family, not really to worship. (You get the same thing at bar mitzvahs sometimes.) The times I have been very uncomfortable at Christian services were when I was surprised by something -- for example, showing up to a "memorial service" for a friend and only then finding out that it was a full Catholic mass, and not one like I had ever seen before. (When they asked everyone to take hands and sing some hymn to Jesus -- I forget which -- I found an urgent need to be elsewhere.) When I know what to expect, I'm not bothered and even find myself doing the anthropologist thing. ("Oh look; there's kedusha.")
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I gather, reading through this entry, that you weren't raised Jewish (I'm pretty sure you've been so the times that I've met you), and I wonder if that might not play an additional role as well? (Just talking off the top of my head here).
no subject
I gather, reading through this entry, that you weren't raised Jewish (I'm pretty sure you've been so the times that I've met you), and I wonder if that might not play an additional role as well? (Just talking off the top of my head here).
That makes sense (and yes, you're right about my background). There's probably also more risk of me doing something reflexively that, if I thought about it, I definitely would not do now -- because it was habit at some point in the past. So even though this hasn't actually happened, I'm spending cycles on preventing it.