[[Sister, Thank you for your answer to my last question. It was very helpful. If you don't mind though, let me ask for clarification on one point. I asked about diocesan hermits and you referred to those professed under c 603. Are there any other Catholic hermits but who do not qualify for non-profit status? Could "Joyful Hermit" the author of the blog I cited be a different kind of Catholic hermit who therefore doesn't qualify for 501(c)3? Does the Church verify a person's standing and eligibility in such cases?]]
Thanks for the follow-up questions. The simple answer to both of these is no. Catholic hermits may be solitary (c 603, what is called "diocesan") or belong to religious congregations (institutes). Either of these kinds of hermits may establish themselves or their ministries under 501(c)3 --- (in the case of a hermit who belongs to a congregation, the congregation might establish themselves in this way). There are no other hermits who qualify to be called "Catholic Hermits" because there are no others who are publicly professed or consecrated; at the same time then --- there are no other hermits who may qualify (qua hermits) for 501(c)3 status.
Yes, such standing, whether of a solitary hermit or a congregation of hermits, requires (and such hermits are able to supply) the Church's verification of consecrated status (canonical standing) --- hence, for instance, the affidavit diocesan hermits are given at perpetual profession/consecration identifying them as hermits of the Diocese of ____. This does not mean merely that they are a hermit with private vows living in the Diocese of ___. It means they represent eremitical life in the name of the Church, are thus publicly professed, consecrated, and commissioned in this specific local Church under the canonical supervision or jurisdiction of the hermit's Bishop; they may, therefore, become 501(c)3 or establish themselves publicly in other ways (including wearing a habit, for instance, or styling themselves as Sister or Brother). Folks in private vows, including priests and lay people who are living as hermits may not set themselves up as 501(c)3 hermits/hermitages because they do not live their eremitical callings in the name of the Church (that is, they are not called, vowed or dedicated and commissioned as well as supervised by the Church per se).
As you may remember, there are three avenues to eremitical life in the church today. The first two are canonical and involve consecration (initiation into the consecrated state) by God through the mediation of the Church. These are 1) congregations of hermits in canonical communities and 2) solitary hermits professed and consecrated under canon 603. Both are public and ecclesial vocations which represent some expression of the eremitical life lived in the Church's name --- the Catholic eremitical life. The third avenue is non-canonical or privately dedicated eremitical life (either lay or clerical).
These "third avenue" vocations may be lived alone as solitary hermits (most common) or in communities of hermits (less common) and are important vocations; they may well be sterling expressions of eremitical life that speak especially well to other lay persons who may underestimate their own call to prayer, holiness, silence and solitude, or their responsibility to live countercultural lives for example (this situation is often a tragic holdover from times when the lay vocation was not adequately esteemed and was played off against supposedly "higher" vocations like consecrated life); thus, these vocations possess great dignity and the Church esteems them highly. Even so, as noted many times here, they do not represent instances of the consecrated state of life nor do they represent "ecclesial vocations" per se which can thus use the title "Catholic" to refer directly to their eremitical life, their congregational standing, or their commissioning by the Church -- e.g., Catholic congregations, Catholic Hermits, Catholic theologians, and so forth. Such hermits are Catholic and hermits, but they are not Catholic Hermits. Think here of the analogy of a police officer living in San Francisco and working for the SMPD and the City of San Mateo; such an officer is not a San Francisco Police Officer.