It depends on what apps it's recommending you update. If you update the core Amazon apps on the Fire (Audible, Kindle app, Music, Gallery, etc.), you'll run into a problem since those Fire apps are different than the generic android apps and are merged into the Fire's launcher. If they're third-party apps, you should be fine. I use 1mobile market as well, but I have app notifications and automatic updates turned off so I don't run into problems on my Fires by accidentally updating something I shouldn't. Just update the ones you need to individually.
The reason you're getting notifications about them is because some of the apps in Amazon's app store aren't updated as much as apps in 1mobile, so they're older versions. Also of note is that sometimes you'll run into an issue with apps on 1mobile that might not work properly on the Fire since it runs a forked version of android. I haven't found this happening very often, and usually it's with a random game or two.
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