Why are non-Catholics allowed to attend all of mass?

I learned recently the name "mass" comes from the Latin "misa" which means dismissal. In the early church in Rome, the preparation portion of the mass could be attended by all, but then when it came time to sacrifice the Eucharist, all non-Catholics were dismissed. > To remain until the missa or dismissal of the catechumens, is easily changed into: to remain for, or during, the Missa of the Catechumens. When the discipline of the catechumens was done away with, and there was only the one connected service, it was called by the long-familiar name, Missa, or Mass. -- "The Latin Mass Explained", Msgr. George J. Moorman My question is what changed to allow non-Catholics to now attend the sacrifice portion of the mass? What were the original concerns that kept them out, and have these concerns been addressed in some way?