These communities have no canonical authority to institute third orders since the communities themselves, with some exceptions, are not canonical members of the religious orders that they represent. Here is a case where epikiea has no applicability. These "third orders" are realistically just groupings of lay persons who privately practice a rule modeled on that of the canonical third orders (re-named secular orders in the 1983 Code) and affiliated with groups of priests and laypersons in private vows who likewise live in community modeled on the rules of the first and second orders of religious orders. In short, everything is a matter of private commitments to communities with private vows.
Now, here is the funny thing. I am a professed brother of the Third Order of the Society of St. Pius X. Canonically, however, the SSPX cannot have a third order since there is no first or second orders. The SSPX are not canonically a religious order, i.e., it is not a community of vowed, regular clergy. Neither are the brothers and sisters of the SSPX monks (or friars) and nuns, rather they are active congregations. The SSPX argues that it is a congregation of common life without vows, a kind of secular clerical institute. Ipso facto, such an institution cannot have a third order since third orders pertain to regular clergy, i.e., proper religious orders. The Third Order of the SSPX, were it ever canonically erected, would be in fact a confraternity, not a third order. This canonical reality is reflected in the statuses of the lay associations affiliated with the Fraternity of St. Peter and the Institute of Christ the King.
Sometimes we nomads of Tradistan engage in some serious LARPing.