Shakey, you can create a new gmail account that you use only for purposes such as this.

Within that new email, you can create a "forwarding" rule that forwards all incoming email to your real-world email that you want to keep discrete.

That way, you'll see the emails coming to the new account without having to "check" the new account.

When you do a reply, you can make a decision about replying from your real account, if it's to a known entity that you're comfortable sharing your identity with, OR if you'd prefer to keep anonymous, just log into your cutout account temporarily.