Lebensreform is not about capitalism per se, but about appropriateness of Lebenswelt to the physical and psychological needs of human Being, ie. the horrible working and living situations that arose in the early days of industrialisation. Essentially, it is a turn against everything that makes humans sick and is tied only to their life circumstances, ie. can be encountered actively by nutrition, sports, different work and living settings, social and (if to one's liking) spiritual engagement. I'd be very careful to put more into it, since it can take (and took) fascistoid twists of imposed, unified ("superior") values quite fast then.
Understanding Lebensreform as I just did, I would deem there can be a case for Heidegger as providing arguments for such a movement. I am more skeptical when it comes to Gadamer, as he essentially is the one who turned Philosophical Anthropology and Lebensphilosophie back into rationalistic thought patterns. I would rather think Plessner and, when it comes to the more spiritual aspects of Lebensreform, Scheler, are better addressees here.
As of vaccination, I would be even more careful. There is a mingling of anti-capitalism, contemporary Lebensreform, and far-right movements who are unified under the "we are just critical/skeptical"-banner but essentially adhere to and spread conspiracy theories. One may think about how companies are allowed to make money out of it as one wants but vaccines are the single most important factor of improved health and life duration over the last 150 years. We could (we could not, a significant part of the world population would die horribly in famines before that, btw) all live "happily" on our farms (who's to say "we" want that and who is "we"?! -> danger of turning into fascistoid thinking), working hard every day to have something to eat and die earlier due to simple bodily attrition, we'd still have (and had) horrible diseases which wiped out significant parts of the human population time and again before we invented vaccines.
I know the latter is a rediculum and it should be taken with a pinch of salt. I just wanted to point out that there is a slippery slope if we romanticise pre-industrial life as the only possible physically and psychologically appropriate Lebenswelt - as many adherents of Lebensreform did and still do. It should not turn into essentialistic thinking of what "the human life" has to be like. The plasticity and indeterminancy of human life is, after all, a central part of the human condition (pace Plessner).
(Disclaimer: I think vaccination should be and remain a personal choice, and at the same time that it is a choice which affects the health and bodily integrity of all of us, since a certain quota is needed for them to be effective. Thus, if someone decides against it for whatever reason, they shouldn't be surprised if others decide that what has consequences for the rest should have consequences for them as well)