This is a great question. As a coach, you're responsibility is to your team and making sure they are making improvements. There will be parents who will say or suggest to you that their child should be getting more attention, special treatment, or more playing time. The best way to handle parents who are rude and/or loud is to listen to them and hear them out. As a professional, it's best to listen first before speaking especially since parents want what's best for their child at all times.
From there, talk to the parent(s) and let them know what your philosophy is as a coach. (I'd suggest doing this early on and have a meeting just with the parents so that they know what your philosophy and goals are for their children). From there, you're laying down the foundation on which you'll want the season to play out. Whether that each child has their own goal; either making improvements, having a new friend, or trying something new they haven't done before.
As a reminder with rude or loud parents,
1) Listen first before responding. Take your time before you respond.
2) If you don't feel comfortable in that situation, walk away or find someone who can provide assistance just in case.
3) Remind them that this opportunity is for their child, as well as other children on the team. For each child to grow, give them the same opportunity and experience as everyone else.
Being a coach is a tough, but very awarding experience. Seeing the growth, impact, and pure joy in a child accomplishing something is extraordinary. You'll always have a critic, but the only one that matters is yourself and the members on your team.
Hope this was helpful, Kyle!
Sean recommends the following next steps:
After you sense that you have fully listened to the parents that are being rude or loud, I would recommend asking "Anything else?" This question can serve to deescalate a situation. In addition, the answers that come to this question can reveal the parents deeper concerns or issues about their children or the situation. This way when you do respond your response can more effectively address the heart of the matter not simply their surface reaction. The parents will be more inclined to feel that you are on their side with this approach.
In addition, I would recommend becoming familiar with Marshall Rosenberg's teachings called Non-Violent Communication or NVC. NVC works well in developing excellent communication skills in any relationship but it is especially effective in a sensitive situation. Part of what is so effective about it, is that when we speak in "I" statements rather than "You" statements regarding our feeling and needs, followed by effectively making requests about what we need from others, we greatly increase our odds of being heard and received.