Few pointers.
One, practice at home. Use your imagination and imagine that your toilet is just a cubicle and everyone outside can hear you. In this controlled environment, practice and practice. The important thing is to associate relaxation with it.
Two, similar to the above point, visualize yourself going to the toilet full of people and finding it relaxing. Do this over and over again, visualize.
Next, do fake it till you make it bullshit. You are an alpha male, you are going into that toilet to assert your dominance. Walk in there with confident body language and blast it all out, intimidate the other faggots in the toilet. Do this in a toilet cubicle first while standing up, and then in a urinal away from people and then eventually, weeks/months down the line, right next to someone.
The problem here is overthinking. Unconsciously taking a piss isn't a problem to your brain, the problem is when you start consciously thinking about it and thus fucking up the process. I'm not going to tell you to "not think about it" because that's easier said than done. Also, ironic rebounding exists, which means if you try not to think about something, you'll think about it even more. So instead of not thinking about it, think about something else. Focus your attention on trying to hit a certain spot in the toilet or something, or just imagine a waterfall or anything like that.
Don't be worried about what other people think, believe me, they don't give a single shit. At most you'll be in their mind for a few seconds and then you'll be forgotten. They have their own worries and problems to deal with to have time to pay attention to strangers.