neutrino VS parity-bitcoin

Most of them use Neutrino https://github.com/lightninglabs/neutrino

You mean this?

You can run a bitcoin node on a phone today with Neutrino for example.

I'm curious about what made you reach that understanding. My guess is that you either tried or heard from someone who tried to open channels with Bitrefill or another LN giant. You shouldn't do that. Big channel operators don't want to dilute their liquidity with unreliable small channels. You should instead connect to a smaller channel that is connected to that big node. LN is all about routing.

Also in the thread's context we are talking about Visa and Mastercard banning merchants right? In a scenario where the LN is widely adopted that merchant can setup and run https://btcpayserver.org and maintain his own independent LN or on chain payment process system.

As for users, there has been work to facilitate nodeless operation on software wallets. Probably based on https://github.com/lightninglabs/neutrino. I know Blue Wallet is building something based on Rust's lightweight LN node so people can establish channels from their personal wallets https://github.com/BlueWallet/rn-ldk.

LN development is really fast paced. I recommend people try to at least learn about the latest advances before making critics like "I've checked months ago and it was terrible".

I wonder if Nakamoto, or Neutrino can be used with c-lightning

You may want to look into this: https://github.com/lightninglabs/neutrino

Lightning neutrinos will thank you. :)

parity-bitcoin. Bitcoin in Rust. Includes support for Bitcoin Cash. Official client is in C++.

parity-bitcoin had shown little interest in using libbitcoin-consensus (which could be problematic when using it for mining/consensus) - https://github.com/paritytech/parity-bitcoin/issues/404 . SPV clients can avoid thinking about much of this. A Rust light-client might get some more uptake.