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Technically, I would say they are both correct.

If you do not handle the changeover to HTTPS properly, you would likely lose all of the site's rankings. If you do everything properly in the changeover, you should not see a loss in rankings, but you still could see some temporary bouncing around for a few weeks.

My main concern is having the not trusted badge in new versions of chrome and firefox, I think chrome even asks you to click a button to proceed.

Seller said cloudflare is a good workaround for this, anyone have experience with this? I see they have a free version.

Changing from http to https will affect your site in the beginning and it may shake your rankings but at the end your site will come up with positive results and as https increases trust factor of users, it is also recommended by Google. So, you dont need to worry much!

Changing http to https, initially it can create problem for for ranking, after somedays later there wont be any problem. Another thing is https is more secure than http. And this is approved by google so there wont be any problem.

there will be slight changes perhaps dancing in your ranking given if you have applied the proper 301 redirects and the content stay in tact.

Yes, off course it may or may not harm your website.

Nope. It's safe to do so. It's actually better if you do so. All of your http urls will automatically be directed to https. I understand where you're coming from since I also had the same concern last year. My site is in a way better position now than before. I say go for it!

Sometime, if you transfer to https then
You will definitely gain benefit from this.