Obviously, we should respect the religion and the beliefs upheld but what about those who are not Catholic and would wish to continue to gamble?
If you believe that they should be respected, then let them talk rather than questioning them. In fact, you are even free to express your opinion, view, and perspective. The final decision depends on the implementing body.
Does religion have the right to be included in conversations regarding gambling if their beliefs cloud their judgement?
It could if they are invited during the conversation. But if not, then they don't have it. But if you see them in the conversation, that certainly means they are invited to make their bold opinion on this matter. They could speak, but as I've said, the judgment depends on how they deliver their arguments. In a place like the Philippines, their voice could be heard because of their numbers and could also influence the decision.