Hi, not a Christian or solo adopter, but wanted to jump on and say fingers crossed for you!
The livestreaming thing I would personally err on the side of caution unless you knew BPs were low or no risk. We found out that BP somehow knows about our appearance, and possibly has a photo of us from somewhere, and they shouldn't know anything, so I wouldn't assume that anonymity is guaranteed. We avoid publicising ourselves as much as possible- so we go to loads of events, but we specifically ask to not be photographed, ask strangers filming in the park to delete videos if they linger on our kids faces etc. Nothing certifiably paranoid, but it is 100% not a risk we take if we don't have to. It would worry me being livestreamed if I didn't know who could be viewing it.
I wonder whether there are some sort of faith based adoption training that you could ask for your minister to access to support them in understanding your needs and the needs of the child? Like a virtual schools but for pastors 🤣 I have literally zero experience or knowledge of that, but I feel its the kind of thing a faith based agency might have contacts for. It takes the pressure off you having to explain or justify certain ways of parenting that might seem counterintuitive to what you are suggesting might be a slightly more conservative crowd. I can only compare it to our local children's centre, who were woefully unprepared for anything LAC or adoption related, and we had to work through processes together. It would have been easier if they had a vague understanding of what was and wasn't allowed as pre adoptive parents. Your situation will be trickier because you will go from being a foster parent to a pre adoptive parent to being an adoptive parent, with different permissions and needs at each stage, which is particularly marked for religious status. It would be highly inappropriate for the minister to suggest certain things before the AO has been granted, for example, and they might not know that, and the burden shouldn't be on you to have to explain it to them.
I would definitely be checking your agency policy about taking L.O to church. When we were in some adoption training groups, it was impressed upon us very much that names and religions couldn't be altered, and that taking a child to a place of worship not sanctioned by BP was not ok in EP situations. Combine that with lots of the support network being through church, and this being difficult to maintain if you can't attend regularly, it might be tricky. Is there someone who could look after baby so you can go if BPs don't agree? Do you have a specific plan in place to explain to a potential LO why they get to go to church with you now/didn't get to go for the first possibly 2 years (if the proceedings take that long), and how that might be different to BP? I assume you have thought of all of these things as part of your approval. It sounds like it is a big part of your identity and planned identity as a family so is worth safeguarding and planning for appropriately.
In terms of comments about marriage, I would hope that most are made in ignorance not malice, but a few prepared pointed responses might give an indication about something being either on or off limits. The other adopter people in church might also give you an indication of who might be likely to make an unfortunate comment and either intervene on your behalf or prepare you so you aren't taken aback. I would hope nobody would be judgemental about the adoption, but some people do have weird views, especially if the family is non traditional. The "it's such a shame that they won't grow up with a ... " or "how will they learn about...." comments are the most irritating for me! If you are attending church, I would assume it is a denomination that is at least a tiny bit cool with single parenthood (or you wouldn't be going there!), so adoption shouldn't be any different. I mean, you could get into a theological debate, but that's not your responsibility, your job is to make sure your kid feels happy and safe, and not ostracised because of some weird comments from other people who have nothing better to do than make comments about a small person and the one who has committed to being their family! We also found that most people don't make malicious comments to your face anymore because who even does that? It's either behind your back and reported second or third hand "just to let you know", or ignorant comments that can be annoying but either corrected or brushed off in context.
Fingers crossed for you and the placements you are considering!