Factors influencing a nominal variable

Thank you in advance for your assistance in this!

I have a dataset set up with a variable, agreement (coded 0) or disagreement (1), for each case with several other possible factors in that agreement. These factors are continous or nominal in nature.

My desire is to find which factor does influence the agreement.

I tried to run a logistic regression, but due to missing variables, the analysis used only 60% of my cases. Some significance are borderline.

Is it valid instead to run a series of t-tests and chi squared for each factor vs agreement? Would this be fishing? Can I just lower my threshold of significance to 0.01 to accommodate this? I do find more significant outcomes this way.
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