[Victor D]

You may have "Disable anonymous checkout" option in your general settings enabled
Also you possibly need just hide login information, not to remove it completely
Try to do somethin like this in your skin1/main/register_account.tpl

{* Anonymous account *}

<tr {if $active_modules.My_module ne ""}style="display: none;"{/if}>
<td align="right">{$lng.lbl_username}</td>
<td>&nbsp;</td>
<td nowrap="nowrap">
<input type="text" id="uname" name="uname" size="32" maxlength="32" value="{if $userinfo.uname}{$userinfo.uname}{else}{$userinfo.login}{/if}" />
{if ($reg_error ne "" && $reg_error ne 'A' && $reg_error ne 'F' && $reg_error ne 'I' && $userinfo.uname eq "" && $userinfo.login eq "") || $reg_error eq "U"}<font class="Star">&lt;&lt;</font>{/if}
</td>
</tr>

<tr {if $active_modules.My_module ne ""}style="display: none;"{/if}>
<td align="right">{$lng.lbl_password}</td>
<td>&nbsp;</td>
<td nowrap="nowrap"><input type="password" name="passwd1" size="32" maxlength="64" value="{$userinfo.passwd1|escape}" />
</td>
</tr>

<tr {if $active_modules.My_module ne ""}style="display: none;"{/if}>
<td align="right">{$lng.lbl_confirm_password}</td>
<td>&nbsp;</td>
<td nowrap="nowrap"><input type="password" name="passwd2" size="32" maxlength="64" value="{$userinfo.passwd2|escape}" />
</td>
</tr>
{* /Anonymous account *}

In the highlighted lines change My_module to your module name
The another option is to transform these inputs from "text" to "hidden"