The problem with both sentences:
You should not let yourself be arrested by the authorities so that
his sacrifice would not have been in vain.
You should not let yourself be arrested by the authorities so that
his sacrifice would not be in vain.
is mainly one of meaning. It's hard to understand what you meant to say, especially with those two negatives. Additionally, there is a problem with tenses.
"so that" can be used to express result or purpose. Considering the use of "would", it might be inferred that the meaning intended to be expressed is one of purpose.
For "would" to work with "so that", some past form (in this case, a past modal) is required in the main clause, for example:
- You should not have let yourself be arrested by the authorities so that you would have somewhere to stay. (This could be the case of a homeless person who, lacking a better place where to stay, preferred to be taken to prison, and is being criticized for having let themselves be arrested for the purpose of getting some accommodation.)
Now, if a present form (in this case, a present modal) is used in the main clause, "will" will be used in the clause of result (the meaning will be the same as above but from a present perspective):
- You should not let yourself be arrested by the authorities so that you will have somewhere to stay.
Note: If you clarify what you meant to say, maybe I can fix your sentences so that they can convey your idea in a grammatical way.