Unable to access university website due to software update requirement on MacBook and iMac

Have you contacted your university IT support folks?

It may well be that you are using version(s) of the OS and/or browser that need updating.

Exactly which iMac and MacBook are you using? We need to know the year and model of each.

Find that info at  > About This Mac.

We also need to know exactly which version of macOS is being used on each computer. Find that info at the same location and above.

If you are using Safari, and your Macs are so old that they cannot run recent versions of macOS, that could be the issue. The current major version of Safari (26) requires macOS 14 (Sonoma) or higher. The one just before it (18) requires macOS 13 (Ventura) or higher, and so on.

Some Web sites (especially banking Web sites) check which browser, and browser version, you are using, and will complain if you are not using a recent version of one of the browsers that the IT people feel like supporting. Maybe your university Web site is one of them.

If that is the issue, installing and using a third-party browser might be a solution. But again, it would be helpful to know exactly which Macs and versions of macOS you are using.

Please read the following user tip and restate your question/problem in detail: 

     Writing an Effective Apple Support Communities Question - Apple Community

What systems are you running on the iMac and MacBook?

Have you installed and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac?

Without your telling us the Mac models and their macOS versions, we are guessing. That seldom has a good outcome.