Can adding bad entropy to good entropy, make a system insecure?
If you have a variable with maximal entropy, and you combine it with an independent variable with less entropy using Xor or modular addition you will still have maximal entropy.

If you have two independent variables with low entropy and you combine them in the above fashion the result will be a variable with more entropy than either the original ones

If however the variables are correlated all bets are off. Even combining two maximal entropy variables may result in 0 entropy (constant variable ) when adding/xoring them.