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. (Canon 964 §2)
Now here's the bit that some people don't know. The priest can also insist on the use of a fixed grille. Here's the original text from the Vatican Website. It's in the section for the Pontifical Council for the Interpretation of Legislative Texts, under the heading Interpretationes Authenticae. (I give a translation below.)
Can. 964, § 2 (cf. L'Osservatore Romano, 13-14 luglio 1998, p. 2)Now here is the (unofficial) translation:
Patres Pontificii Consilii de Legum Textibus Interpretandis, in ordinario coetu diei 16 iunii 1998, dubio, quod sequitur, respondendum esse censuerunt ut infra:
D. Utrum attento praescripto can. 964, § 2, sacramenti minister, iusta de causa et excluso casu necessitatis, legitime decernere valeat, etiamsi poenitens forte aliud postulet ut confessio sacramentalis excipiatur in sede confessionali crate fixa instructa.
Summus Pontifex Ioannes Paulus II in Audientia die 7 iulii 1998 infrascripto Praesidi impertita, de supradicta decisione certior factus, eam confirmavit et promulgari iussit.
+ IULIANUS HERRANZ
Archiepiscopus titularis Vertarensis
+ BRUNO BERTAGNA
Episcopus titularis Drivastensis
The Fathers of the Pontifical Council for the Interpretation of Legislative Texts, in their ordinary meeting of 16 June 1998, determined that the question (doubt or "dubium") which follows should be answered as below:
Q. Whether, keeping in mind the prescription of canon 964, §2, the minister of the sacrament, for a just cause and excluding the case of necessity, may legitimately decide - even if the penitent strongly demands otherwise - that sacramental confession should be heard in a confessional constructed with a fixed grille.
The Supreme Pontiff John Paul II in the Audience on 7 July 1988, granted to the President mentioned below, having been informed of the above decision, confirmed it and ordered it to be promulgated.
+Julio Herranz, titular Archbishop of Vertara, President
+Bruno Bertagna, titular Bishop of Drivasto, Secretary
So - priests or people - don't let anyone tell you otherwise!