They mean two different things. "What do you like to do?" Means what do you like to do in general on any given day. "What would you like to do?" Is more of a question about what you want to do right now. Neither is more polite. "Would you like" is the more polite version of saying "do you want".

"What do you like to do?" Is a question like what does the person like doing overall "What would you like to do?" is asking what would you like to be doing at this moment, like right now. Since they are different neither is really a polite form, i mean both are polite, it's just that they are the same level of politeness depending on what you ask.

They are different questions, so we can't really say one is more polite (although, generally, "would" adds a level of politeness). Asking "what do you like to do" is similar to asking someone about their hobbies, or interests. Things they enjoy doing in general, and not at a specific moment. Asking "what would you like to do" is asking someone what they want to do now or in the near future. It's asking for a plan, an idea, or a suggestion. Hope this helps!

What would you like to do? Is more polite.

What would you like to do?