How to start vim without executing /etc/vimrc?

From the Vim man page:

-u {vimrc}

Use the commands in the file {vimrc} for initializations. All the other
initializations are skipped. Use this to edit a special kind of files.
It can also be used to skip all initializations by giving the name "NONE".
See ":help initialization" within vim for more details.

If you still want your ~/.vimrc to be processed, try this:

vim -u ~/.vimrc

Add the following line to ~/.bashrc (or your shell's equivalent file if not bash) to have the -u switch added automatically:

alias vim="vim -u ~/.vimrc"

You won't be able to add something to ~/.vimrc to prevent /etc/vimrc from being read, because the system file is processed before your user file (see ":help init", section 3, "Execute Ex commands, from environment variables and/or files").

From the Vim man page:

-u {vimrc}

Use the commands in the file {vimrc} for initializations. All the other initializations are skipped. Use this to edit a special kind of files. It can also be used to skip all initial- izations by giving the name "NONE". See ":help initialization" within vim for more details.

So this should do the job:

vim -u NONE

You should be able to alias this to your normal command for everyday usage.