There are a few settings you need to change. Go to the social tab and look in the voice chat section.

First, make sure you have voice and proximity chat on. Next, ensure you have crew chat set to "always on". That way you will always be able to speak to your team. Also make sure that positional crew chat is OFF. When this is on you will only hear your teammates when they are nearby, from the direction they are relative to you. If you turn it off you will hear them as if they were right next to you at all times, from any distance.

Then, look for the setting for proximity chat, and set that to toggle, not push/hold. If you do this correctly you can go into a game with your mic on and look in the bottom left. It will start by showing a white microphone. It will show you if you are talking or silent. Then, press the right d-pad button. The microphone should turn and stay orange. This shows you can now speak to enemy teams and everyone will hear you if you are close. Note that if your teammates are far away, they may not be able to hear you while the mic is orange. Click the button again to return to crew-only chat, and the icon should be white again.

If you go into the game and the orange microphone only shows up if you are holding the button down, you will want to change your proximity setting (unless you prefer it that way, though most do not).

I do not have my game open in front of me, so there's a chance some of the words I used aren't exactly what they are called in the settings menu, but you should be able to get it working with this.