If the new software updates aren't compatible with my current MacBook, must I buy a whole new one?

Are you currently running macOS 10.11 as shown in your equipment profile? If so, and the computer is Mid 2010 through Late 2011, it can be upgraded to OS 10.13 "High Sierra" which has better browser support than 10.11. Even if the High Sierra version of Safari is losing support by some sites, FireFox still runs on 10.12 or higher and is fully supported by most web sites.

You can find the important sub-model of your Macbook Pro by doing 'About this Mac" from your Apple menu:

If you tell use the sub-model, we can tell you the newest OS you can install and how to do that.

ziggybur224 wrote:

If the new software updates aren't compatible with my current MacBook, must I buy a whole new one?

You have to buy a new computer if the old computer no longer supports your computing needs. Your old computer will continue to work but it will not be able to run newer apps.