8 .
Given how outwardly similar Mass appears to a communion service in many Protestant churches, and indeed how pivotal its central commemorative meaning is to all sincere participants, it may seem surprising that non-Catholics are not allowed to share in it. (There is no such reciprocal prohibition ~ i.e. by Protestants on would-be Catholic co-communicants ~ but most strict Catholics wouldn't 'let themselves go', however friendly and well-intentioned the ecumenical circumstances, because the Vatican prescribes one absolutely crucial difference.) So... what is it that Protestants, by definition, would themselves not be able to accept within the Mass?
While Catholics recognise seven Sacraments (of which Mass is one), Protestants, for instance, reject Penance (Confession etc.) as an absolute precondition. Therefore in the eyes of the Catholic church, they are not fully and willingly subscribing to all that the Catholic (= 'worldwide') fellowship as a whole subscribes to, on Rome's own terms
Non-Catholics, again by definition, are not obliged or minded to accept the binding and infallible authority of the Pope. Therefore, however much inclusion, forgiveness etc. he and his priesthood may preach, outsiders may not engage fully in the communion ritual on his 'turf' or terms
There are elements within the Catechism of the Catholic Church ~ i.e. its declared set of doctrines which members must know, confess, recite and generally abide by ~ that non-Catholics would not have subscribed to, over and beyond the difficulties identified in Answers 1 and 2. If anyone is not in complete agreement, assent and understanding with an organisation (and may therefore be disqualified, by omission or commission ~ e.g. not having been to the Confessional), they cannot expect blithely to go through the motions, on at least somewhat false (& hence inherently sinful) pretences, of the most sacred and special ritual of the Church
(Click this Answer only if you believe all the three preceding ones are applicable, and/or if you can't reach a decision between them!)