When you love someone with anxiety, do not get weirded out when they ask you to approach a cashier for them or make a phone call for them or walk into a restaurant before them. Do not make them feel like there is something wrong with them for needing help in social situations. Do not make them feel guilty about remaining inside of their comfort zone because there are certain days when they can break out and other days when speaking to a stranger is downright impossible.
When you love someone with anxiety, do not get into arguments with them over how quiet they are being around your parents or your closest friends. You might wish they were more comfortable around the people you care about the most, but they have the same wish. Do not make them feel like they disappointed you because that is their biggest fear. They do not want you to feel like you are being held back by them. They do not want you to grow to resent them. They do not want to be a bother. They care more about how you feel than about how they feel, so realizing you are unhappy with the way they handled a situation will be devastating to them.
When you love someone with anxiety, you might not understand how they are feeling, but you should be respectful of those feelings. You should not accuse them of overreacting. You should not tell them to calm down. You should not roll your eyes and shake your head. You should try to see where they are coming from. You should consider their emotions valid. Just because you do not share their fears does not mean their fears are silly. Just because you have an easy time introducing yourself to strangers and mingling at parties does not mean those things come easy for them too.
When you love someone with anxiety, do not make them feel stupid, because they already feel that way. They already feel like something is wrong with them. They already feel like an outcast. You should not worsen those fears. You should not intensify their insecurities. If you cannot handle a relationship with them, leave. Do not stick around to make them feel bad. Do not send them on guilt trips. Do not cause more harm than good.
When you love someone with anxiety, you should make them feel comfortable. Allow them to express their vulnerability. Let them know it is okay to cry in front of you, it is okay to rant in front of you, it is okay to fall apart in front of you. If you make them feel like you only want them around when they have their shit together, then they are going to feel like they have to censor themselves around you. They are never going to let their guards down completely.
When you love someone with anxiety, accept their anxiety. Realize it is part of the package. Do not fault them for something they cannot control.