Cyril Burt removed, g factor would still be something that is taken very seriously in psychometric testing. Even when you strip all the racists and eugenicists out, g is still there in the statistical analyses and its presence is uncontroversial. The statistics say it's there. This factor hasn't gone away with time or repetition.
Modern, high-quality intelligence tests built and normed by scientists who are keenly aware of IQ testing's dark roots demonstrate the g factor as well. Those norms are matched to the test taker so they know how you did compared with people your same age, gender, race, ethnicity, socioeconomic background, educational background, etc. So a lot of the old, really bad problems are much harder to have now. Believe it or not, we are better scientists now than we were in 1909. It's not to say that there aren't still problems, but I do mean to say that comparing a top of the line, modern intelligence test to the early work of the eugenicist set is a lot like comparing a supercar to a turnip truck.
The question now is one of how the factor is derived - essentially, if the g factor is one thing that operates across many types of problems, or if it's actually many different types of specific intelligence modules, each operating only on one specific type of problem, thereby explaining why the g factor seems to be more active on some tests and in some areas rather than others. How you get there instead of to a unified g factor involves a lot of very advanced statistics and mathematics but it can be done.
A good intelligence test now, like the Stanford-Binet will also provide subscales so you can see where you were comparatively better or worse, in some general categories like spatial reasoning, verbal reasoning, numerical reasoning, etc. Whether intelligence is one thing or many modules, you can still see and compare your abilities across types of problem, so the theoretical issue doesn't actually matter much at the point where the tests contact the public.
The other thing to remember is that IQ testing like all psychometric testing is an indirect measure, and that makes it weaker but we have to be careful not to heap all indirect measurements into the "pseudoscience" category. It cannot access what is truly in your brain, and it is forced to rely on repeatability, concurrence, and prediction for its validity. Modern intelligence tests - good ones - agree with each other pretty closely about how they score the same person, how the same person does over time, and they generalize and predict results in other fields fairly well - not fantastically, but say, moderate to high-moderate depending on what you want to look at.
Modern, high quality intelligence tests like the WAIS-R and the Stanford Binet are completely different animals from their predecessors, and we're much better off for it.