First, just because one couple does it, doesn't mean that it's a new "trend". (I get this was likely a tongue in cheek comment, but it is a pet peeve of mine when people make generalizations on society based on what one (or even just a few) people do.)
As for the envelope with no RSVP, I do see how that comes across as a soliciation and I think you're fine to be put off by it. I would be. That said, do you know for sure that is what it is? It may be a faux pas for sure, in that the intent of the envelope and what guests are supposed to do with it aren't clear, but is your neice someone who is generally tacky? Has she proven to be a gimme-pig in other ways? These things hardly just show up for the first time at a wedding invitation and I'd be hesitant to assign that kind of rudeness to someone based off of one envelope (especially where the intent isn't clear).
As for requesting money/gift cards in lieu of gifts, I can see where this could be an issue. I've always been taught that registry info on an invitation is a "no-no". Yet, recently I've heard that it is now acceptable. So I don't know. I've heard of couples forgoing the traditional wedding registry in favor of cash, gift cards, and chairity donations in the past....even asking for contributions to help pay a honeymoon (which I personally don't like). As for requesting gift cards, I don't really see this as any bigger of an issue than requesting specific gifts, as a registry does. Either way, the couple is still asking for something specific...be in monetary or merchandise...
The issue would then be is it acceptable to say this on an invitation? And I don't know the answer to that, though I suspect not. And I would say that is a faux pas.
ETA: When DH and I got married, we were also doing some major home renovations. We already had just about every household item one would need (in most cases double), so we didn't register at all. We never said anything in the invitation about registries or home improvement, but many people asked us (and my parents) for registry information. We were honest and said we didn't really need anything that we could register for, just stuff that we were fixing up. So our needs were like (wood, paint, plumbing fixtures, etc). We ended up getting a lot of money and gift cards for this at our wedding, which we were very grateful for and we told our guests what project their contribution was helping us finish in the thank you cards.