Never quite understood the HN fetishism about keeping emails and phone numbers private. I hand them out like candy and haven't felt a price for it.
Also, my phone number is known to some identity providers I trust. If they sent me an SMS asking me to click a link, I might be inclined to follow that link. This is quite right despite the sender being very easily spoofable because nobody but these identity providers know my phone number.
No. I'd rather be very careful with that number.
Of course you could be phished or tricked by SMS but to expect your number to be private is to expect everyone ever who you give the number to go to extreme to keep it private as well.
If you ever gave your number to someone who downloaded an app which has permission to contacts your number is no longer private (Facebook has taken big advantage of this, I'm sure there are less than reliable apps that took bigger advantage).