can I host a mail server on my home server and use cloudflare tunnel.

No. IPs of cloud flare are blocked on most email servers and you really need port 25 be opened. Also residential IPs are in PBL lists, which also used on email servers to get rid of army infected PC. If you going to get intermediate proxy, choose them carefully due to a lot of cheap (or with bad reputation) hostings are rejected (or has much more spam score) too

Currently that’s not possible unless you have business internet.

Basically ISP can mark whole IP ranges as residential, so any email sent from those is marked as spam no matter how you set it up…

It’s cheaper to pay Google or similar $6 per month and avoid the hassle of locally hosted mail server.

Possible - yes.

Do you want it? Probably, no. Especially, SMTP. Better use something like Zeptomail (cheapest) for delivery.

You can still self-host the receiver.

Mandatory do-not-self-host-at-home notice: custom domain at skiff.com is free, iCloud+ Mail is $0.99 and Zoho is $1.25/mo.

Yes you can do it but from what I hear without being a big company your chances of not being blacklisted are high. I wouldn’t bother personally.

I’ll preface this by saying I host my own email, but I don’t host it at home. I’ve also entertained the idea of running a tunnel to bring it in house (although not with cloudflare). You’re going to run into 2 main issues that I see:

1. I only did a brief search so I don’t know if there’s documentation narrowing the range of ips that are used for tunnels, but cloudflare publishes this list of IP ranges that they own. By my calculation that’s a little over 1.5M addresses and you don’t have any control over what IP is being used when sending out email. This means that you have to add every one of those ranges to your spf record. It also means that if one of those IP addresses does land on a blacklist you have no control over whether or not outgoing mail will be sent from it, and for 1.5M addresses that’s a pretty substantial risk.
2. I don’t know how you plan on using email, but for me email needs to be reliable. I can’t have emails I send getting dropped and I always need to be able to receive email. This is one service that, essentially, there’s no maintenance windows on. It has to always be up. That is something that’s extremely difficult to do at home. At a bare minimum your risk profile is just your ISP provider. Residential connections generally don’t have SLA agreements. This means that if they it’s going to go down for an hour or two for maintenance that’s outside of your control. Or if there’s a storm that takes down the utility lines, there’s no guarantees in place about how quickly that can get fixed. And again that’s the bare minimum: you also have to think about always having power, hardware failure, software failure, software upgrades, etc. There’s a lot that goes into making a service have a high degree of reliability and the reality is that it’s exceptionally hard to do at home.

As u/apperrault said though, technically this is probably possible to do.