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Standardization is nice for people who make sites and people who use them.
Which is why we have HTML5, CSS3, and JavaScript, supported by all major browsers.
Unless you're doing something outrageously non-standard, there is no reason to block specific browsers.
Except for politics.
These terms are absolutely meaningless. Browsers like all Chromium forks and Firefox add new CSS, HTML and JS features on a almost monthly basis. Safari then usually is takes a year more to implement them. And for the past few years Chrome has usually been adding new stuff the fastest, then Firefox a bit later and then Apple adds them after a year, but only if they don't threaten the native Apps on iOS because of AppStore money.
Web standards keep evolving, this is normal. Otherwise you would be still running Adobe Flash.
Safari is the new IE?
That's not what a web site is though. That's just an application with a network api.