Does moving your peep height change your sight tape? I moved my peep up and resighted my sight in. Now when I move the slider to 60 yrds I am shooting high. Did moving my peep cause this? I’m new to using a slider.

Yes, moving your peep height will require you to adjust the sight tape you're using on an adjustable pin sight. As you found out, it usually won't affect things at closer distances, but as you move further out you will begin to notice things being off.