Should I refuse to be named as co-author of a low quality paper?
First, if you think the manuscript is not worth submitting even after major revisions, or in other words, if you as a referee would recommend its rejection, then the answer is clear - you shouldn't be coauthor.

However it seems that you evaluate the manuscript as ok-ish, and the main concern is that its content is somehow outdated. I would do what your old group asked you to do: review and possibly improve the paper. Do this to the maximum extent you can - given the fact that your are likely busy with other tasks and research - and then leave the main responsibility to the first author and your old group.

After all, you are still a young student / researcher. This paper could be your first entry in your publication list, and some more time and more papers have to come before you get concerned about your papers being all of the very best quality. A published paper normally cannot be too wrong, and various journals can accommodate different quality or differently tailored papers. So perhaps try to influence also the choice of where to submit, especially to avoid a non-ending revision phase.

At this stage of your career, you can only benefit from a published article. To those who read it, it will show that you actively entered the research of a group even when you were younger than now. To the rest of the community, it will be just a publication. And that is better than no publications. 

The main point is how much you can improve it, and if there is space for it. As a "publish as it is" decision seems to be highly unlikely, you must be prepared to work on it further. But again, leave the responsibility to the group from which the research originated.

See it as an opportunity to publish, and not as an annoyance. 

The above applies to a salvageable manuscript. For a better and definitive answer I should be a specialist in your field and evaluate the manuscript myself.

Rejection would also fix the issue. Although I always tried to avoid rejection even as coauthor, I don't think it should be your concern at this stage. Nobody will know except the referees, and even they won't blame or remember you. 

edit: I want to make clear that the recipient journal should not be a predatory one, or one with such a low reputation that is not worth working to publish therein. The above answer assumed this.

Also, above I wrote " A published paper normally cannot be too wrong, and various journals...". Beside that "normally" means what should be the normality, this doesn't mean that errors and, even worse, frauds, have no room in literature. It must be seen a concern for the whole community and is not related to the OP situation. If the manuscript will be accepted, it will most likely stand as an acceptable paper, indeed. Not to say that the manuscript is in the hands of the OP. With this respect, the paper cannot be too wrong already. Otherwise there wouldn't be this thread.