Anyways, how bad of an idea is this if it is a bad idea?
This is a matter of balancing your own intellectual interests with your career goals. In terms of career goals, not only is it probably not so bad, it's actually probably a good thing; it looks great at this stage and later on if you have experience in multiple areas, as this will increase your breadth of expertise and your ability to collaborate with other researchers down the road.
However, in terms of your intellectual interests, you must carefully decide how much you are willing to sacrifice. It may be that you are only passionate about topic X, and working on anything else you would just not be happy. Or it may be that you are flexible, and you would in the long run be just as happy working on topic Y. Also note, that switching to topic Y now is likely (but not guaranteed!) to mean that later on down the road, at least if you are successful in Y, that your research interests evolve and become more related to Y. That could be a good thing or a bad thing, it is up to you to decide. Above all, you should never choose to work on something that you have no passion for.
Also, is it generally assumed that by accepting an assistanceship in a specific subject that I'm also planning on doing my thesis in this area?
You should check with your program (how many years away is your thesis?), but likely yes. It could also be a flexible blend of topic X and topic Y; have you talked to the professor about your research interests? Are they willing to mentor you even though you want to retain some interests in topic X? Are there possible opportunities in the future to do some research that is "between" X and Y?
I've never seen a graduate student that did work unrelated to their research
This is very surprising, because in my experience this is extremely common. While you may think that graduate students were always "set" on the topic they work on, in actuality many of them who work in some field actually started out in another field, but then started working with a professor and ended up switching trajectories. Research interests often inevitably evolve. Keeping an open mind with your research interests and directions, if you are willing and happy about it, can be a huge asset in academia as it opens up the number of possible professors that you can work for.
and that lack of overlap with my own intererests might increase my workload.
Yes, this would be true if you continue research X while working on Y with the professor; that is something you should talk to the professor about.