This option is available if the AirTag is a family members' AirTag. You can ignore alerts indefinitely under those conditions.
Aside from my partners' AirPods which are bugged up (unique to them specifically, not sure...) I've ignored alerts on all her other tags.
When you receive the tracking alert, tap it and you will have a few options. One of those options is to ignore alerts. When you tap it, it will ask you whether you want to Pause Tracking Alerts for the day or indefinitely. If you tap indefinitely, you'll stop getting alerts for that item.
You can see this referenced on Apple Support [1], but I've done this personally with success. The only devices it doesn't work on are AirPods but it works on my Chipolo wallet card and all my/their AirTags.