Phone numbers and email address are NEVER shown to the public with the sign up sheets plugin, so there is no privacy/security concern there. The public doesn’t even see full names for sign-ups. Since people can’t always be trusted to type their email correctly, a phone number is a good alternate means of contact, and a much faster method of contacting volunteers if something changes at the last moment.
However, I will keep this here and consider adding another option to make the phone field optional.
If you don’t want the automatic reminder emails, you simply don’t enter anything in the reminder fields when you create a new sign-up sheet and no reminders will be sent. If you do that, then the only emails that get sent are a confirmation email right after they sign up, along with a notice email to the committee chairs. That’s pretty standard for signing up for anything via the web, and any one who marks those emails as spam clearly has some issues.
Also, on a related note, you can install an SMTP plugin on your site to make WordPress use a SMTP email account to send outgoing emails, which you could then configure to use a Gmail or other off-server email account to send emails if you are worried that your server will be shut down for simply sending sign-up confirmation emails.