Hi

To my knowledge, you don't stop it from crawling through the button (like a nofollowed link), rather you block the robot at the page it ends up on after clicking submit.

Say the user hits submit and it takes them to mydomain.com/confirm.html  On that page you'll want to add;

....if you want it to NOT index the page but follow the links on it.

or

...if you want it to NOT index and NOT follow the links on that page.

Its advised that its better to do this with the meta tag than in robots.txt.

Hopefully I've understood the question correctly!

-Dan

Your other option is to use meta robots tag like this;

Its a one step process instead of two.

Full documentation on URL removal from index here and on the robots meta tag here

I'd look at this in a holistic manner.  If your site looks great, functions great, has good information, promotes trust among visitors, has good on page optimization, etc this is likely not of concern.  The search engines know that an e-commerce site is going to have many add to cart buttons on a page and on a site.  I'm sure they take this into consideration when judging an e-commerce site. As long as you're not doing anything sneaky with the buttons like hiding text behind them or anything, I'm sure your fine.

Of course, an example of your site, screenshot or link, is always most helpful when determining these things

-Dan

Yes, you can try Screaming Frog. Free up to 500 page crawl, or you can buy the pro version.

Hi Gary

Believe I just answered something similar here

-Dan