Safari Won't Load Certain Websites on Your 15-Inch MacBook Air
Since the same URLs work in Chrome on your 15-inch MacBook Air, Safari on your 13-inch MacBook Air, and your iPhone, we can narrow this down considerably. A general website or home-network problem is unlikely. The focus should be on Safari's settings, extensions, or software affecting the 15-inch Mac.
Rather than trying every possible fix, follow the steps below and use each result to decide what to do next.
Start by Checking the Error
When Safari fails, note exactly what happens. Does it display “Safari can't open the page,” show a blank screen, load indefinitely, say the website is blocked, or load the page without videos or other content?
The error matters because a connection failure, a content restriction, and a page that won't run properly can have different causes.
Test a Private Window
Press Shift-Command-N to open a Safari Private Window and try the same URL.
If the website works: The problem is more likely related to stored website data or an extension. Continue with the checks below.
If the website still fails: Disable Safari extensions next.
Disable Safari Extensions
Open Safari >> Settings >> Extensions and turn off all extensions temporarily. Quit Safari using Command-Q, reopen it, and test the URL again.
If the website now works: Re-enable extensions one at a time until the problem returns. You've identified the likely cause.
If it still fails: Continue to the new-user test.
Apple guide: Safari extensions on Mac.
Clear Website Data if Appropriate
If the Private Window works, open Safari >> Settings >> Privacy >> Manage Website Data. Find the affected websites, select their entries, and click Remove. Test again.
This clears stored data for those sites without erasing your entire browsing history. You may need to sign in again.
If the Private Window works but clearing website data doesn't help, revisit the extensions and individual website settings.
Test a New Mac User Account
If the problem persists after disabling extensions, create a temporary standard account under System Settings >> Users & Groups, if permitted. Sign in, open Safari without installing extensions, and try the same URL.
If the website works in the new account: The problem is likely associated with your usual account, such as its Safari configuration or user-specific settings.
If the website still fails: Focus on software or settings affecting the whole Mac, including security tools, content filters, and possible Safari or macOS issues.
Investigate System-Level Filtering
If Safari fails in both accounts, check for VPNs, antivirus software, parental-control applications, web filters, or configuration profiles that might interfere with browsing.
Because Chrome works on the same Mac, a general DNS or network issue is less likely, although some filtering tools can affect browsers differently.
If Safari explicitly reports that a website is restricted, check System Settings → Screen Time → Content & Privacy for web-content restrictions. Don't assume a restriction is responsible just because adult websites are involved; use the error message and test results to guide the investigation.
Apple resources: Screen Time on Mac and Safari troubleshooting.
Update macOS
If the problem affects both user accounts and no filtering software explains it, open System Settings >> General >> Software Update. Install any available compatible updates, restart your Mac, and test again.
The Fastest Way to Narrow This Down
Given that the same URLs work on your other devices and in Chrome on the affected Mac, I'd start with just two questions:
Does the website work in a Safari Private Window?
What exact error or behavior do you see when it fails in normal Safari?
Those answers will help determine whether to focus on Safari's extensions and stored data or move directly to testing the Mac's configuration and system-level software.