I do not use Olympus but I can offer a general statement: most auto-white-balance systems are pretty good, but are inherently limited by three issues - (1) "white balance" adjustments are aimed primarily at a color temperature, which presumes a light spectrum which is fairly smooth; artificial light other than incandescents are not smooth but have very discontinuous spectrums, (2) many lighting systems flicker, and besides changing brightness during the cycle change color, so the camera may correct well but by the time the shutter opens the light is different, and (3) your scene can be confusing to a system; imagine a florescent lit scene but with daylight from a window lighting a part of it, so that there is no single right setting.
None of these are easily handled by any kind of filters. Mixed lighting can be somewhat mitigated, e.g. gels on strobes to cool or warm the flash to match natural lighting.
There are two approaches that have the most leverage, one you discounted (mostly) which is post processing. In post processing you not only can adjust white balance, but apply it selectively over areas of the image that may be lit differently. Shooting raw gives you a LOT more leverage in post processing for white balance adjustments.
The other (that is complementary not exclusive) is a custom camera profile, assuming your camera shoots raw. While this also requires shooting raw, it does not require human attention to apply. If you produce a custom camera profile for a specific lighting venue, it can be applied to all shots in that venue at once. This does NOT correct white balance errors, but it does help correct color distortions due to unusual spectra (e.g. lighting that may have too little green would see green emphasized to adjust).
Another complementary approach is to look for a camera which has "flicker control" (may have different names). This is mostly available in higher end cameras, but it tracks the actual flicker of the lights, and opens the shutter only to coincide with the brightest point. This is not so much about being bright, as being consistent - instead of pink/green/whiter cycling you get only the whiter, which then can have more uniform white balance adjustments applied. A couple minutes with google did not show me any Olympus MFT with flicker control but I did not look carefully, plus that changes over time. Sports oriented cameras in particular are adopting this feature, as flickering lights in arenas and stadiums are a real problem there.
My recommendation, if you can do any post processing at all, is to (1) shoot raw, (2) plan on a brief look and adjustment on a calibrated screen to correct where the camera misses, and (3) if you shoot the same venue frequently consider a camera profile (and software, like Adobe, that supports it). If you can't post process at all (as in human review), shoot raw anyway, run through a good ACR, and trust the auto-white-balance. That way if you get that really spectacular shot and want to improve the colors after the fact, you have the raw image to provide extra leverage. Some cameras will shoot raw and JPG at the same time.
I should also mention that a manual color balance is a possibility, but one I mostly discount as (1) flicker kills it in many places, (2) unless you are shooting in one spot in one venue it changes depending on subject and where you aim and background. It is useful if you can work it in to have a neutral grey card in view at the edge of the shots, provided you can get it in identical light. You can use this as a quick reference in post processing. But be aware it might not work perfectly, as you may be amazed at the difference just a few feet can make. I shoot basketball (as an example), and the white balance varies hugely by whether a player is down near the floor (e.g. scrambling for the ball) or up high shooting, primarily due to the warming effect of the yellow floor proximity. Many venues are like that, with a lot of variation over short distances.