People are indeed accustomed to seeing pilgrims in the churches and sanctuaries along the Camino, but accustomed doesn't mean that everyone is is happy with the way some pilgrims dress, particularly in the smaller villages. Locals here and along the Camino do sometimes comment on the lack of respect shown by pilgrims who enter churches dressed as if they were going to the beach.
My opinion is that it's never a bad idea to be respectful and "err on the side of caution" as it were.
That doesn't mean that you have to pack clothes especially for going into churches, or add a lot of weight to your backpack, but I would encourage you to avoid wearing tank tops, tube tops and really short pants when visiting churches, sanctuaries or monasteries, and especially if you plan to attend masses in the evening. Lightweight hiking t-shirts that cover the shoulders and are made of high tech fabric that "breathes" and "Capri" pants that come to just below the knee are what I use. They're plenty cool and comfortable while walking, light in the pack, easy to handwash and give no cause for offense when entering a church or monastery.
For women, another very simple solution is a lightweight, cotton wrap-around skirt and a shoulder wrap. These can be whipped out of your pack in a flash and thrown around your shoulder and waist. Plus, as Peronel pointed out above, even in summer the churches can be quite chilly, so these have the added advantage of helping ward off the chill.
But really, for attending masses, if you just pack lightweight hiking t-shirts that cover the shoulders and "Capri" pants that come to just below the knee, there won't be any problem at all.