You could work with your pastor to establish reasonable guidelines for your parish, and then your pastor could share them with your diocesan bishop and encourage him to consider them as possible guidelines for the whole diocese, as well as share them with his brother bishops throughout the country.
Some people complain about the casual attire that others wear at Mass, particularly Sunday Masses. But that’s not strictly about modesty, although encouraging parents and young people to avoid jeans and t-shirts is a worthwhile endeavor.
Regarding men and modesty, a parish could encourage them to avoid looking like they’re coming from or going to a pick-up basketball game and thus not wearing tank tops and shorts. In the summertime, it has become common for men to wear dressy shorts, but those should be knee-length or close to it. (St. Peter’s Basilica in Vatican City prohibits the wearing of shorts altogether, but that might be best left for a longer-term goal vs. an initial requirement.)
In any event, our clothing should not be a needless distraction for our brothers and sisters at Mass. In addition, men should avoid wearing tight or form-fitting clothing, which can also be a needless distraction for others.
For women, low-cut tops should be avoided, particularly those that expose a woman décolletage region, including her pectoral region. In addition, skirts worn at Mass should be knee-length, as with guidelines at Catholic schools, including because they tend to move upward when a woman sits. One could also recommend the avoidance of dresses that expose a woman’s backs, although wearing a shawl can overcome that issue. Ditto, with a dress that exposes a women’s shoulders, although some may debate that requirement. And form-fitting clothing, as with men, should be avoided.
The bottom line is that we can wear our Sunday best without being a needless distraction to our brothers and sisters in Christ.
Regarding enforcement of any proposed parish dress code, that needs to be left to the pastor and pastorally inclined people he designates, with men speaking to men and women speaking to women, including to the parents of non-adult young men and women vs. the young people themselves. In addition, if someone is a family member or genuine close friend, they could say something. Otherwise, those concerned about a particular person should speak to their pastors or persons the pastor has designated.
Finally, regarding those who leave Mass right after receiving Holy Communion, the parish pastor can make a periodic announcement, realizing (and noting to the congregation) that some people might have to leave Mass early for reasons of employment or periodically for some other good reason. But, again, one shouldn’t presume to correct someone on their own, unless they are a family member or close friend.
For more on modesty in clothing, please see my colleague Michelle Arnold’s article.