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Odd braking symptom...is this dangerous?

The speed sensors on my 2000 silverado went bad about 6 months ago. I could not afford to replace them so I was advised that I could remove the abs sensor and solve the issue of the abs kicking in when it shouldn’t. That has worked well. Now there is a new issue. The brakes are still working properly, but there does seem to be a little bit of extra play before the brake pressure starts if the pedal is depressed quickly. If is is depressed slowly, there is no shuddering. The shuddering is in the pedal only. There is none in the steering wheel, and no vibration in the wheels. The shudder will even happen while the engine is idoling and in neutral. If I depress the pedal very slowly, there is no reaction. The braking ability dies not seem to be affected, just how the pedal itself is responding. Any ideas or thoughts?