If you are conservative, you aren’t necessarily a card-carrying member of the Republican party (though you might be); it means you resist change.
Conservative has the word conserve in it, which means to hold on to, or save. In a drought, you want to be conservative in your water use. If you don’t get paid that much and don’t want to use credit cards, you’d better be conservative with your money. When we talk about environmental conservation, we mean the protection of natural resources.