I hate that this may sound as a bombshell but it’s really not. Just for precautionary thinking. While open access data such as from the Fox Insight is commendable for reuse and analysis, I am eager to share some musings for consideration.
The first is the dynamic nature of the gut microbiome. Although thought to mature early in life, its composition is influenced by diet, disease, medication, etc. Even in the absence of disease, these factors (diet, exercise, stress, etc) shape the periodic composition of a healthy gut. So, the question is, does a one time point data collection do justice for estimating a healthy gut?
The second is peculiar to matching cases from a cohort to [independently sampled] controls, of course age and sex matched. A paper in press from one of my labs collaboration with the MicrobiotaVault Inc. showed significant clustering [beta diversity] in the gut microbiota of healthy stool samples from five different countries from different continents. Apparent healthy gut looked different for each group. Does this engender the need to relook at data harmonization and standardization? How do we handle diversity inclusively?
I agree that longitudinal data in general is usually the stronger approach, since for example in your example it’s quite clear that the gut microbiome can vary a lot over time and a single sample may not fully capture an individual’s “baseline” state (whatever that might be). At the same time, I also think practical limits like cost, logistics, and participant burden mean that cross-sectional studies still have an important role, especially when paired with careful metadata collection and harmonisation.
Maybe the real challenge is figuring out when longitudinal sampling is truly necessary and when a well-designed one-time snapshot is still informative 
Based on the experience of that paper in your group, how do you think we should draw that line? I can imagine there are so many factors you can practically collect?
Maybe the future will be to have some sensor as close as possible to the person, such that it’s more practical to collect more interesting and useful data, hopefully in some private way.
… Or maybe we need to think about noninvasive proxies? You reminded me of this study (unfortunately only going on in the US) where they want to track the first atlas of “intestinal gas”! https://www.flatus.info/
Well, I think longitudinal should be the go to, whenever possible, and findings from cross-sectional data interpreted with the right pinch of salt it deserves. Nonetheless, longitudinal data collection is not funny, at all 
It seems like a very challenging data collection problem, as there is not just the question of longitudinal microbiome data collection, but also those confounding factors you mentioned like diet, exercise, and stress. Perhaps there is a role for pairing microbiome samples with wearables data, with the aim of characterizing those associations under healthy conditions? This could provide a baseline for understanding which impacts are disease-related and which are environmental/sociological/lifestyle. But it seems like a tough sell to collect such data from a large enough healthy population, who are perhaps less motivated to contribute to research than those with specific diseases!