I've never really identified with a particular denomination so that wouldn't worry me, although I'd be interested to know what prompted the change. I suppose it would also depend on whether the person had specifically changed denomination or simply started attending a church that was associated with a different denomination.
If someone stopped attending church entirely I'd be concerned for them. I don't believe that someone who stops attending church has necessarily abandoned their faith - a few months ago I stopped attending church because the church I had been going to had become toxic - but if someone has been hurt by attending church I'd want to see if it was something I could help with, or help guide them towards another church and maybe meet with them periodically while they tried to figure everything out. Often it seems small groups of believers gathering is more like church should be than dozens of people meeing in a building where nobody plays any meaningful part in the proceedings.
Abandoning the faith entirely is a tricky one. I think the best thing to do there is to give someone a safe space to talk. Much of the time the response from people in the church is to try and talk them back into it, which can frequently come across as some variation of "sit down, shut up, and listen to me tell you why you're wrong" and then we wonder why the person doesn't listen. This kind of situation is a major reason why I believe people need to know what they believe and, crucially, why they believe it. If someone is having crushing doubts about their faith it really doesn't help them to be presented with little more than a robotic "God is faithful, click, whirrrrrr.... God is faithful, click, whirrrrr...... God is faithful" response from someone whose faith has never really been tested. It feels like talking to a book.
It's easy to judge someone for the decisions they made, but we seldom know what choices they had available. It's easy to look at a situation and comment that "I would have (insert textbook ideal response)" but for the person who chose a different path it's reasonable to assume that the textbook "correct" response wasn't a desirable option for some reason. Whether they were thinking rationally or out of desperation makes little difference, they chose the option that was the most appealing to them at the time. Chances are they know what the textbook "correct" response was, so simply telling them that "I would have chosen the correct response" is unlikely to be helpful and will probably drive them further away. It makes more sense to understand why they chose a different response.
