You can remove fields that are displayed in the profile.
Go to:
ACP ÂÂÂ » PCP Wizard ÂÂÂ » Add / Remove Page Fields
But it might help more if you stated what exactly you want unchangable. I hate giving broad answers <img>
Also, you can override user option in:
ACP ÂÂÂ » General Admin ÂÂÂ » Configuration +
[Edit] - Keep in mind the profiles aren't denied access just because you removed the link to the profile.
http://www.SITENAME.com/profile.php?mode=editprofile takes you directly to your profile unless you have a page permissions mod installed and set to deny that page from registered members. Which isn't included stock in 1.4.0. There is a link to it on this server. I believe I was the one that asked about it at one point, but I never got it installed. (Link to thread:
http://integramod.com/forum/viewtopic.php?p=1272#1272)