You are describing someone like a baptist preacher who has a family to worry about. We are not speaking of protestant clergy, but dedicated Catholic priests. A Catholic priest should NEVER decline confession to any Catholic.
Better check canon lawâŚ
not all priests may hear confessions (except for immanent threat of death situations), and without the bishopâs permission, ordered priests may only hear confessions of those within their community, or living with their community yet not members (as sometimes happens).
CIC:
Can. 964 §1. The proper place to hear sacramental confessions is a church or oratory.
§2. The conference of bishops is to establish norms regarding the confessional; it is to take care, however, that there are always confessionals with a fixed grate between the penitent and the confessor in an open place so that the faithful who wish to can use them freely.
§3. Confessions are not to be heard outside a confessional without a just cause.
So, no, in the store is NOT canonically allowed, unless some good cause exists (like, for example, a penitent who is unable to attend due to work schedules).
CIC:
Can. 966 §1. The valid absolution of sins requires that the minister have, in addition to the power of orders, the faculty of exercising it for the faithful to whom he imparts absolution.
§2. A priest can be given this faculty either by the law itself or by a grant made by the competent authority according to the norm of â can. 969.
Note: orders alone are NOT enough!
CIC:
Can. 967 §1. In addition to the Roman Pontiff, cardinals have the faculty of hearing the confessions of the Christian faithful everywhere in the world by the law itself. Bishops likewise have this faculty and use it licitly everywhere unless the diocesan bishop has denied it in a particular case.
§2. Those who possess the faculty of hearing confessions habitually whether by virtue of office or by virtue of the grant of an ordinary of the place of incardination or of the place in which they have a domicile can exercise that faculty everywhere unless the local ordinary has denied it in a particular case, without prejudice to the prescripts of â can. 974, §§2 and 3.
§3. Those who are provided with the faculty of hearing confessions by reason of office or grant of a competent superior according to the norm of cann. â 968, §2 and â 969, §2 possess the same faculty everywhere by the law itself as regards members and others living day and night in the house of the institute or society; they also use the faculty licitly unless some major superior has denied it in a particular case as regards his own subjects.
So, if his bishop grants the priest permission to hear confession, he may hear confession until itâs revoked.
CIC:
Can. 968 §1. In virtue of office, a local ordinary, canon penitentiary, a pastor, and those who take the place of a pastor possess the faculty of hearing confessions, each within his jurisdiction.
§2. In virtue of their office, superiors of religious institutes or societies of apostolic life that are clerical and of pontifical right, who have executive power of governance according to the norm of their constitutions, possess the faculty of hearing the confessions of their subjects and of others living day and night in the house, without prejudice to the prescript of â can. 630, §4.
The list of who can do so by the law itselfâŚ
- Bishops of a diocese or exarchate, by being bishops of a place, have authority to hear confessions. (Ordinaries, §1.)
- Pastors, by virtue of being Pastors, have permission by the law to hear confession in their parish or from their parishioners. (Pastors, §1).
- Acting Pastors, while serving as such, have the faculty of the pastor. (§1)
- Superiors of an Order: only those in their order, or residing in their orderâs facilities, may have their confessions heard.
NB

by canon law, only priests and bishops can be Acting Pastors or Pastors)
CIC:
Can. 969 §1. The local ordinary alone is competent to confer upon any presbyters whatsoever the faculty to hear the confessions of any of the faithful. Presbyters who are members of religious institutes, however, are not to use the faculty without at least the presumed permission of their superior.
§2. The superior of a religious institute or society of apostolic life mentioned in â can. 968, §2 is competent to confer upon any presbyters whatsoever the faculty to hear the confessions of their subjects and of others living day and night in the house.
Bishops and Religious Superiors alone grant faculties to other priests besides ordinaries, pastors, acting pastors, and religious superiors.
CIC:
Can. 970 The faculty to hear confessions is not to be granted except to presbyters who are found to be suitable through an examination or whose suitability is otherwise evident.
proof that not every priest is suitable⌠canon law says so!
CIC:
Can. 971 The local ordinary is not to grant the faculty of hearing confessions habitually to a presbyter, even one having a domicile or quasi-domicile in his jurisdiction, unless he has first heard the ordinary of the same presbyter insofar as possible.
No granting faculties to other Bishopâs priests unless youâve checked with the other bishop.
Refs:
vatican.va/archive/ENG1104/__P3F.HTM
vatican.va/archive/ENG1104/__P3G.HTM
Bottom Line: Canon Law is clear: in the proper place, with the proper priest, unless something is very strange.