Should I care what my parents think?

There are lots of fathers who have the same controlling habit. Mostly, they do it out of love and care for the child, rather than a deliberate attempt to interfere in their lives. You should still tell your dad when you make major decisions. You should do so out of respect for him. And make him aware that you'll not do anything bad that would bring his name into disrepute, or shame on the family. Plus your telling him is for his information and not to solicit for his views.

I think that at this age, you're mature to take every decision for yourself. Nevertheless, don't ignore the advice of your father completely. Parents normally have a lot of wisdom to share about most of life's issues. Maybe you'll see the wisdom of his counsel later on in your life, or when he's dead and gone. But do well to seriously consider some of his proposals. There may be issues that his opinion would actually benefit you.

I hope this helps.
Good luck!

Just tell him. If he doesn't like it, he doesn't have to visit.

You should bear in mind that the prefrontal cortex doesn't reach full development until you're out of your early twenties, so while you are legally recognized as an adult, that doesn't necessarily mean that you are as mature and responsible as you'd like to think you are. Technically, you pretty much still have the brain of a teenager. Based on that, I think you should listen to your father. However, you don't /have/ to; you've been on your own for five years, so decision-wise your dad's opinion should pretty much be out of the picture. I definitely wouldn't advise you to change your mind about living with your boyfriend based on the fact that your dad won't like it.