Yes, it would be interesting to hear from those who are directly concerned by this, i.e. those who manage and provide staff for non-commercial albergues such as donativo albergues, municipal albergues and parochial albergues.
There is an analysis by a European Travel Agents and Tour Operators Association (the analysis deals exclusively with data protection aspects and not with the additional administrative burden) which states that the new law, not yet applicable, concerns
lodging activities open to the public and regulated by the corresponding sectorial laws - it is anyone's guess what these corresponding sectorial laws are. But whatever is exempt from these sectorial laws is also exempt from this new traveller registration law. For those who are exempt, the current traveller registration law will continue to apply as it is not suspended. Apologies for stating this, everybody will have read it themselves of course in the BOE.
At the end of the analysis, there is a list of possible actions. I don't know the date of this paper. As to their "Other actions": At least one question had been submitted in March 2023 (by C. Puigdemont and others btw) and there is a written answer; it does not say much. Another written question was submitted last month by two Spanish MEPs from the PPE and, as usual, there will not be an answer any time soon.
Like most of this stuff, this analysis paper is just yet another press release: