Should I speak to someone who does not return a greeting of peace? Thank you.

If a man refrains from returning the greeting of salaam because you are a foreign woman, his action is correct according to the majority of scholars, as they hold that a man should not greet a foreign woman, nor should she greet him. And if someone offers the greeting, they are not entitled to a response, unless the woman is an old woman who is not desired. However, if he is a mahram (definition) to you or if you are a woman, the sunnah (definition) of greeting does not cease, even if you think he will not respond, due to the general command to spread salaam. In any case, it is not permissible to speak with him if there is a fear of fitna (temptation or discord), but if there is no such fear and it is for a beneficial purpose, it is not prohibited.