The Muslim should avoid places in which Allaah is disobeyed as much as possible. Hence it is better for you to support Islamic stores which do not sell things that Allaah has forbidden, and advise their owners to supply things that you need, because that will benefit all concerned, you and the store owners.
As for buying what you need from the stores asked about, there is nothing wrong with that in sha Allaah, especially when there is a need for that and these items are not available in other stores that do not sell haraam things.
But you should go to those stores only as much as is necessary and the more you can avoid entering them, the better.
It should be noted that obliging non-Muslims not to show alcohol or their religious symbols openly only applies if they enter a Muslim land or submit to the rule of Islam.
But if they are in their own country and have not submitted to the rule of Islam, then dealings with them should be in accordance with their customs and beliefs, and they believe that alcohol is permissible in their religion.
Abu ‘Ubayd narrated that ‘Umar ibn al-Khattaab (may Allaah be pleased with him) heard that some of his governors were taking the jizyah in the form of alcohol and pork, then they sold them to ahl al-dhimmah ‘Umar (may Allaah be pleased with him) said: Do not do that; rather let them sell it, then take (the jizyah) from its price.
Abu ‘Ubayd said: he meant that the Muslims were taking alcohol and pork from the ahl al-dhimmah then appointing Muslims to sell them, and this is what ‘Umar forbade, but he granted a concession allowing them to take [the jizyah] from their price if dhimmis were appointed to sell them, because alcohol and pork are part of the wealth and property of ahl al-dhimmah, but they cannot be wealth for the Muslims. End quote from Ahkaam Ahl al-Dhimmah by Ibn al-Qayyim (1/184).
This indicates that sales of alcohol among Christians are valid, because they believe it is permissible in their religion, but it is not permissible for a Muslim to sell it, even if he is selling it to a Christian.