Can we sync reminders without using iCloud on Big Sur

This kind of defeats the whole intend and purpose of living in the Apple Eco-System with several Apple Devices. Changes on one device get reflected on all other devices. Start a document on one device and pickup immediately on another. Yes, there is a personal preference and some are not comfortable with iCloud. Doing so, just makes thing more work to get everything on one device to another.

Of course, iCloud is not a "server"; the info stored on it is parked in an anonymous server on a server farm. Be that as it may, no, I do not expose anything private (including photos) to any kind of storage I do not have control over. I have an abundance of external drives and I back up my phone to my iMac occasionally - in my case, it is really not necessary since I actually only use the phone to make phone calls. I do not do anything else with it - partially because I have too much trouble trying to read what is on the screen and the tiny keyboard buttons. Usually make a number of missed/wrong key hits if I am prompted for my ID password, so I try to avoid it. So there are no files, pics, or games other than the iOS apps included.

Unfortunately not.

The only thing you might be able to do, which is a bit of a kludge is create screen captures on your device, and use Image Capture to download them to your computer. You can make sure iCloud is not set to sync your photos on your device, and just manage them locally. There are plenty of photo editing apps for the iPad that let you keep them on your device. They just won't be syncing with the Apple Apps themselves.

I don't trust private info to an anonymous online server, so I do not use iCloud - so I cannot and do not wish to sync anything.

For some things, airdrop is an easy way to move things from one device to another. Personally, I do not need to be in the Apple eco-system - my Macbook Air is used mostly for testing and is purposely totally separate. I can download emails when I need to and there are always external drives which can easily be plugged in to copy files or whatever from one device to another. My iPads are for totally different purposes as well, so there is no syncing necessary. If I take a pic with my iPad, I will transfer it to my iMac as soon as possible and possibly delete it on the iPad. My iMac is my "go-to" machine where everything is stored, worked on, edited, filed, and backed up several different ways.

So, you can make not wanting to sync work. Just make sure that you go through all your settings if you should need to reinstall the OS or there is an update or upgrade: Apple has decided that wanting iCloud on and syncing, so it will try to do this automatically as soon as you set up a Mac after an upgrade. I avoid it by refusing to sign in to iCloud; and, after setting up, I immediately check Settings/System Preferences to make sure nothing is enabled. I do have a bit of a problem with the OS/Apple telling me what I should like.

I wouldn't exactly call iCloud an "Anonymous" online server. It is in fact secured by your iCloud account. Otherwise people would be having their iPhones broken into all the time, since iPhone backups are directly to the cloud. The more secure you make your iCloud account the better. Alas MFA is only supported on Mac OS 10.12.4 or later, and newer iOS versions.

I agree though the level of security is a matter of our personal level of trust. I will trust no one who calls me directly to my credit card number. And I don't use my cell phone for those calls.

You do to have to have your iPhone backed up to iCloud (just turn off in settings). You can still pick what you want iCloud to manage.