“Regularity” refers to following the Oblate Rule of Life (“regula” – hence “regularity” is following the Rule and guiding one’s life by it).
A young and dynamic community would attract many people to the sanctuary devotions and sacraments, but also to visit with the Oblates. Eugene here gives an important piece of advice: do not let an exaggerated number of visitors become a distraction to their religious lifestyle.
If the number of visitors is found to be a disturbing factor, steps should be taken to preserve regularity, notwithstanding that. There will be more edification through fidelity like that than from an over-politeness that would entail wasting a considerable amount of time and a lot of disturbance.
Letter to Fathers Guigues and Dassy, 18 August 1834, EO VIII n 484
Advice that continues to be relevant for today: while being close to people we need to keep focused on the witness we should be giving and WHY we are close to them.