After a cancer diagnosis, you move to 'cancerland' and are basically stuck there for the rest of your life. As life goes on you meet new people as do non-cancer people. But the difference is when, and if, you tell them about your medical history and cancer.
Let's tackle these one by one. First of all when you get a new job after cancer, you should never tell your new employer about your cancer even if you get a new diagnosis. They do not need to know. You are not legally required to tell them. If you have medical appointments, they do not need to know why. You can always say something like 'I have an issue that needs to be dealt with'. And if you need chemo or radiation again which will require frequent absences you can just say you have a medical condition that may require alterations in your schedule for a while.
It is your decision if you want to share your medical issues with your employer and, if you do, it will be held against you at some point. No matter that there are anti-discrimination laws, you will be discriminated against. You will become a 'sick person' in someone's mind and will blatantly or subtly become the subject of discriminatory practices. Miss out on a promotion etc because you may not be able to grow with the position or could miss too much work because of your medical issues. So keep your mouth shut.
New friends? That's different. When you feel comfortable in the relationship you can tell them about your cancer if you want. It depends on how open a person you are. And how you think they might react. Some people (because they are idiots) head for the hills at the word cancer, others will wrap you in a protective blanket and try to baby you, and others may try to drive you crazy with their attempts to make you a healthy person by following their misguided attempts to force you to alter your life to that of a grain, eating raw vegan who runs marathons (or anything you are not - I am not against vegans I am just not a vegan and don't want to, nor do I want to run a marathon). Note: none of these people are your friends. The people who are your friends will treat you the same as they did before they knew about your medical history.
Dating? Same deal. I was first diagnosed with thyroid cancer before my freshman and sophomore years. My father called the dean because I was late coming back after summer break because of my surgery. I told a few friends and it was somewhat a known fact while I was in school but I didn't discuss it much. But I did date and tried to be a normal college student as much as possible and didn't let my cancer distract me from normal college student activities such as parties, football games, bar hopping, cramming for exams, staying up really late, and binge watching old movies on Saturdays with a group of friends.
But later on when I was out in the real world, dating was different. Should I tell that hot new guy or not? Eventually I learned that there was no reason to share my cancer history until the relationship got serious. Basically, if they were close enough to me to see the medications I took daily, realized I took more than the average human being, and asked me why I needed them, that might be a good place to start.
I had roommates for years that I never told about my medical history because I just didn't consider it their business. Some boyfriends I told, some I didn't. If it was a short term relationship that wasn't going anywhere, why bother? If a relationship was getting serious, it could become shared information. But it really didn't rush to share the information. Maybe I am a fairly private person but I never have found a reason to rush to share the information, unless I was is at a cancer focused organization or something.
I guess what I am saying is that there is no reason to share your medical history if you don't want to. People don't need to know the specifics unless you want them to.
If you are diagnosed with cancer, it is your choice to share or not. Society has become more open about cancer than in the 1980s when I was first diagnosed, but it doesn't mean you have to tell anyone you don't want to. (But feel free to tell the cop who pulls you over for speeding on the way to your cancer support group. I had a friend did and got out of a ticket.)