The Short Answer: No.
The Long Answer: What you're probably seeing at church are women wearing camisoles and tank tops under their blouses so they don't show their garments. More than just covering up our garments, it's a way that we maintain our modesty, which is something we worked on before we even went to the temple.
The standards of modesty upheld by the world and the ones upheld by the Church are different. Generally, what the world considers modest is usually considered immodest by the Church. That's not to say we're prudes, but we want to hold ourselves to a higher standard. The missionaries might not have explained this standard to you, or may have figured that after attending church for a while, you'd pick it up.
In my personal experience, the rule of thumb in my home was that I wore clothes that I could wear garments under when I eventually received my endowments. That means shirts or blouses with full sleeves, not cap sleeves, and a neckline that doesn't show cleavage. Skirts and shorts reach to an inch or two above the knees or longer. No clothing is tight or revealing in any way. Men also wear shirts with sleeves and shorts that are similarly long, and no clothing is tight or revealing in any way. Most importantly, pants should not sag! That's just dumb! With these standards, garments should not show at all.
But if you haven't gone to the temple to receive your endowments yet, why should you still follow these guidelines? Our bodies are sacred temples. How we treat them shows our respect for God and our gratitude for this precious gift. This includes the way we dress and present ourselves. When we dress modestly, we invite the Spirit's presence and have a good influence on others. If we dress so that undue attention is brought to certain parts of our body, it can encourage thoughts and actions that lead to breaking the Law of Chastity. Better to have the Spirit, I say.
As members of the Church, people are watching us. They notice what we don't eat, what we don't say, and what we wear. In an effort to avoid all appearance of evil, let us dress so that everyone knows that we know we are Sons and Daughters of God, and we have respect for the bodies He gave us.