I am pretty low key, unless drunk, but in almost every aspect of life, including with family, I just can't finish what I am saying if it is over 15 seconds. I am over 50 and used to listening before I talk but it seems now people are waiting to tell you something almost off the bat before you even finish your thought/point. I am pretty boring, so I can concede it might just be me.
Change a dynamic, then see what happens.
(This is not a reflection of you specifically, but a general statement to anyone period, particularly adult males)
1) Change the way you dress
2) Try a new haircut or new hair style
3) Focus on being in peak physical condition/physical shape relative to your situation and circumstances (age, injury, etc)
4) Pay attention to good eye contact, firm handshakes, and posture
5) Impose effective social/communication boundaries
6) Show some indicators of wealth/elevated perceived social status
7) Have a career that is universally "useful" or denotes some level of perceived status within it
In general, nearly all people, particularly Americans, and then again, American adult males in general, will be judged and treated, differently or not, to their status or perceived status. The more the person in front of you thinks you can do for them or be an "asset" to them, the less they want to create social friction with you. They are NOT treating you better. They are NOT respecting you. They are NOT engaging with you in good faith. They simply want something from you or believe you could potentially give them something they want down the road. Someone who cuts you off, talks over you and doesn't listen to you wouldn't do that to Steven Spielberg would they? Oprah Winfrey? Elon Musk? Joe Rogan? Denzel Washington? Their character is the same, but the circumstances changed.
If people are generally "disrespectful" to you, even strangers, and in most circumstances, they don't assess your "status" as a potential asset to them. That's what most adults do all the time, play a game of what they can get out of other people. Why do a lot of women have expensive handbags and shoes? If you ask them directly, they'll come up with some politically correct canned statement. But women treat other women with more "regard" (I won't say it's respect or even civility) when they have signs of status or perceived status. Many women are pretty vicious and mercenary in that way. All? I wouldn't say all. I would however say nearly all that are adults.
So should you or anyone else change certain visible dynamics to suit other people? I would say the first rule of better long term interactions with other people is to cut out all the toxic ones. Low character people are anchors. They will drag you down. You can't negotiate with them. If the negative situations are in the group of family members or coworkers or other obligations, then I'd limit my exposure to them. Don't put yourself in a situation to have a conversation with them. If it's kids, then if it's your kids, I'd squash that immediately. Children don't get to talk how they want to their parents, not when they live under your roof, it doesn't work that way.
But everyone should do whatever they can to raise their "perceived status" situation to the limit of their practical self esteem. It's good for self esteem to workout and be in good shape. It's good for self esteem to dress nicely and want to be as presentable as possible. It's good self esteem to reward yourself for your hard work day to day with sometimes getting an occasional luxury item, that might also show sighs of wealth/status. Don't do things to impress others, do them to show a degree of self care/self love/good self esteem for your own well being. Within that, sometimes those things also have an unintended benefit of getting a lot of people around you to back off or reduce social friction.
You can't change people. You can however walk away from many people. And those where it's difficult to walk away, you can just limit them to the point of nothing else in your life.
On an aside, the best way to be more effective in verbal communication/conversation, is to do more of it. If you have concerns on your "soft skills" in that regard, put yourself in a position to practice. In effect, talk to everyone. When you go a grocery store, or hardware store, or gym, say Hello to everyone you see. When it's near the holidays, wish everyone you see , even strangers, a Happy Thanksgiving and/or a Happy Holidays. Talk to people out of your "routine" and patterns, i.e. people you are commonly interacting with now, and see what happens. Handling people verbally is a very powerful skill set. It only makes your life easier if you can do better at it. So this is a worthwhile pursuit and there's a long term benefit to showing increased effort here.