If you want something other than Adobe, use another software makers' products. But unless you're satisfied with free software you are likely going to be paying more since the other software are not as fully functioned as e.g. Lightroom Classic and Photoshop and so you will need to purchase/license multiple software products to be able to do everything.
Who needs to do everything? I do 2/3 of my photography on film and 1/3 on digital, and I want to keep everything together. LR does three things for me: catalog, RAW conversion of digital files and adjustment of brightness and contrast for scanned negatives, and basic editing like rotation and cropping. I need a pixel editor because I always have dust spots to remove from scanned negatives, sometimes a lot; I use Photoshop Elements 11.
The catalog function I can replace with Nikon View, which is free. Scanning negatives rules out Nikon NX-D, which will only edit images created with a Nikon digital camera. If I shifted to digitising negatives with the ES-2 I could use NX-D, but the ES-2 plus negative holder is $200 or so. Better quality might be a reason to pay for the ES-2 but it is not worth it just to be able to use the free software.
The RAW conversion and negative adjustment
and the pixel editing functions I have shifted to Affinity. It costs 55 euros, and has not had a paid update since first release two years ago. It is, overall, about as good as LR for processing RAW files - better at some things (colour rendition, eg), not as good at others (lens corrections, eg). Affinity is
much better than LR for processing scanned negatives, which was a pleasant surprise - it is not something software reviews mention. It is better than PSE for dust spotting. I can round trip from View easily.
PSE 11 is 32 bit so I would have had to replace it next year anyway. PSE is not an option for subscription (!), so that would have had to be bought as a stand-alone.
So, no, I have not paid more to replace LR, and I get better function in one important respect.