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My mountain bike has 26 x 2.35 tires on it and I am ordering new 26 x 2.125 tires.

Will these be okay to use? What issue might this cause? Or will the difference be negligible?

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Your new tires are a little bit less wide, and thus less high than the ones before.
You will not face any problems, but technically, if you have a speedometer, the readings will be slightly off. With the slightly smaller outer diameter your speedometer will show marginally higher readings at the same speed as before.
And while negligible, and most likely unnoticeable, going uphill will be marginally easier, and going downhill you will reach marginally slower speeds. But all in all, there will not be any real difference, and no problems and issues.

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    Yes, speed calculated from revolutions will have to be calibrated to the diameter in use. Going uphill will be no easier, but you will move all your effective gear-ratios insignificantly towards the lower/easier region (I agree with your point, not the wording). The ride will be slightly harsher/less suspended if at the same pressure. All these changes due to the small diameter change should be negligible/adjustable. Just check that your rims are fine with the new size tire (which they almost certainly will be).
    – WornChain
    Commented Mar 26 at 12:30
  • The change in complete-wheel diameter isn't remotely the most important effect of going to a different tyre width. Compliance and rolling resistance are far more consequential considerations.
    – leftaroundabout
    Commented Mar 26 at 23:15
  • @leftaroundabout while this is true, for the change in size OP is planning, those considerations are about as negligible as what i described. Also, a possible change of tire surface / profile design / rubber mixture could affect rolling resistance a lot more than a 10% change in width. But it all boils down to: 2.35 to 2.125 is a negligible change.
    – Burki
    Commented Mar 27 at 8:03
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    @Burki that's simply not true. A 2.35" tyre has 22% more volume than 2.125" and allows running significantly lower pressure without increased risk of punctures, and that translates to notably better off-road performance. The 1.5% change in outer diameter from ~ 665 to 675 mm meanwhile is negligible unless it causes the tyre to scratch on the seatstays.
    – leftaroundabout
    Commented Mar 27 at 8:51
  • ...That about tyre surface / profile / design / rubber having a large influence too is true, but it doesn't take away from the importance of the tyre width.
    – leftaroundabout
    Commented Mar 27 at 8:54

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