It depends partly on what you do when you keep your mouth open. Make sure that you conduct yourself, whatever you do, whatever you say, in a charitable manner. It's not enough to protest "I love non-Catholics" if you bash them with uncharitable words. We run into lots of anti-Catholics who bash Catholics and say, at the same time, how much they love "Romanists."
If this kind of thing isn't a failing of yours, then we can consider the next point. Should you respect other people's beliefs? You need to distinguish between respecting other people and respecting all or part of their beliefs.
Five centuries ago, should you have respected the Aztec belief in human sacrifice? Today should you respect the New Age belief that many people walking around now used to be princes or princesses in ancient Egypt? "No" to both. Such beliefs aren't worthy of respect because they're simply wrong. (Who would insist that a geophysicist "respect" the belief that the Earth is flat?)
You never should respect error, though you should respect the erring, because God loves them. You should respect whatever is true in other religions. It's not an all-or-nothing proposition. You can reject the errors while respecting the true elements.