Should you publish your podcast episodes on a particular day of the week, avoid the weekends, publish on popular days, or something else?
In short: publish the same day as your previous episode.
(Watch for my next episode and article about the best time of day to publish!)
Consistency is more important than the day itself. Even consistency down to the same minute of the same hour! This is because some legacy systems, including Apple Podcasts, try to learn your publishing schedule so they know when to expect new episodes and can catch them more quickly when you publish.
These kinds of legacy processes (and especially the not-so-smart ones) require a lot of server computing power, but they can be replaced with the much faster and resource-conserving Podping protocol in Podcasting 2.0. (That's where apps and services get pings about your updates within seconds of your publishing the update.)
So first consider what day you can publish on with 100% consistency (except for hiatuses). And don't worry about managing this yourself! All the good podcast-publishing systems let you schedule when your episodes will publish so they can go out “on the dot” and without your presence.
2. Consider your audience
After consistency, think about what might work best for your audience. While content for business people is generally best in the middle of the work week and probably not on the weekends, people are interested in hobbies and entertainment at all times (but may be too engaged in the hobby/entertainment on the weekends).
The point isn't necessarily to publish on the exact day they will play your episode, but to ensure it's ready for them to watch or hear soon after you publish.
However, consistency is still more important because your audience will adapt and might even start to expect your episodes on whatever day you choose.
3. Consider your content
What you talk about might have an inherent schedule or routine to it.
In addition to considering business-focused versus hobby-focused content, consider the rhythm of your topic. For example, a weekly TV show, weekly news wrap-ups, and such.
For subjects that already have a consistent schedule, I recommend recording and publishing your content about halfway between each occurrence. This gives your audience enough time to catch the recurring thing your talk about, enough time to send feedback for your episode, and enough time to play your episode before the next recurring thing happens. Because these things could occur on any day of the week, your podcast about it could also be any day of the week that's around the halfway point, but still consider the other factors I've already mentioned.
If you publish too long after the thing you're talking about, your audience might not have a chance to play your episode, or they might even forget the details of the things you're talking about.
4. Consider your “competition”
Lastly, find other podcasts covering your same subject and consider when they publish.
You'll see studies that show the most popular days for publishing episodes. But that doesn't mean you should publish on those days or even avoid those days. If you're going to look at when other podcasts publish, look only at other podcasts in your same niche and ignore the rest.
You could try publishing before them to try getting your content played first.
You could try publishing after them to ensure your content is unique, cross-references, improves, or is the “last word.”
And you might try to avoid publishing on the same day as others in your niche so your audience doesn't get overwhelmed on that day and choose to skip your episode.
5. Your audience will do whatever they want
Lastly, remember that podcasting is time-shifted, so your audience might hear or watch your episode days, weeks, months, or even years later. And this has little to nothing to do with the “downloads versus streams” debate.
This is why I give these things only as considerations, but consistency is still the most important thing.