Would this be bad to do? What are the consequences? Will I Lose Readers?

I don't think this is a big deal? It's common in my genre for indie authors to jump around between series. I do it occasionally, too.

(Occasionally I hear stories of readers complaining when a book is pushed back and sending nasty comments to an author, though I have not personally experienced this. It may happen to me eventually, but I don't concern myself with it.)

I don't have any direct experience as a writer with something like this, but my first question for you is if the two series have the same audience? If yes, I think you run a risk of derailing the first series by launching into the second. If I were a reader awaiting the 3rd Barney book and saw the 1st Apocalypse book come out, I might wonder if the Barney series was delayed or even abandoned. Do you have a blog or other social media outlet you can respond to their questions?

Actually, I have experience with this as a reader on two occasions. I was enjoying Dean Koontz's Frankenstein series, and it took aaaaaages for book 3 to come out. It finally did, and was as good as the first two. Since it was Koontz I knew it would come eventually. On the other hand, I am still waiting after five years for book 3 of a different series by a different writer, and I've given up hope since reading (four years ago) that the author was re-writing the first two books, which I didn't think needed re-writing. He's not come out with other titles in the meantime, so I can't say if he's lost me or not. I'd read the 3rd book if he publishes it, but I don't know if I'd read the re-written first two if they ever come out.

Chris P said:

I don't have any direct experience as a writer with something like this, but my first question for you is if the two series have the same audience? If yes, I think you run a risk of derailing the first series by launching into the second. If I were a reader awaiting the 3rd Barney book and saw the 1st Apocalypse book come out, I might wonder if the Barney series was delayed or even abandoned. Do you have a blog or other social media outlet you can respond to their questions?

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Yeah, it might be worth putting something on your website, or if you have a newsletter, include it in that. You can make a page on your website for Book 3, for example, and give and estimated release date, even if you don't have a blurb or pre-orders.

Speaking as a reader, I don't have a problem with authors writing multiple series.

What would irk me more is a work that's abandoned, unfinished. (This has happened more than once, unfortunately.)

Yeah, the 'abandoning a series' thing, for me, too.
If your previous books are all stand-alones with the same characters, and there's nothing unfinished left undone, but that future adventures could happen - a standard thing in mystery series, for examples - that's one thing.

But, if the previous books have been going towards a final goal or big reveal, and you walk away whistling, so to speak, yeah, people will remember. I mean, you might do the same with your next big idea.

Some big name authors publish different series under different names. That's something you could consider doing.

Woollybear said:

Some big name authors publish different series under different names. That's something you could consider doing.

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+1, especially if they're distinctly different audiences.

An author name is a brand, basically. Some people put all the stuff under one name and trust the reader to find what they want to read, others focus more on specific targets with specific names. It's up to you if you want all your series under your current name, or if you want to break it up. And it's usually not a big secret, just an acknowledged thing. "That author writes middle-grade humor as Jenny Penny, and they also write cozy mysteries as A. Kay."

One advantage to a different name: more specific targeting of a different audience.

One disadvantage: you'll have to put the work into building up the new "brand" that you put into building your first brand. Granted, you'll have more experience this time around, but it's still a process, and it still takes time and effort (and a little money, if you buy ads or build a separate site.)