.-cx-PRIVATE-ProfilePage__header {padding: 0px 0px !important;}

.-cx-PRIVATE-Shell__content {position: static !important;}

*{box-sizing: content-box !important;}

.-cx-PRIVATE-ProfilePage__header {padding: 0px 0px !important;}
.-cx-PRIVATE-Shell__content {position: static !important;}

Unfortionally links will not clickable. For clickable needs
*{box-sizing: content-box !important;}
but everything will be askew then.

Positive thing: Savefrom extensions will work (generate direct links).

You can see the GET command differs despite the same URL being used.

[code]
Failed load

URL
https://instagram.com/someuserpage/

Request
GET /someuserpage/ HTTPS/1.1
Host: instagram.com
User-Agent: Opera/9.80 (Windows NT 5.1; Edition United Kingdom Local) Presto/2.12.388 Version/12.17
Accept: text/html, application/xml;q=0.9, application/xhtml xml, image/png, image/jpeg, image/gif, image/x-xbitmap, /;q=0.1
Accept-Language: en
Accept-Charset: iso-8859-1, utf-8, utf-16, *;q=0.1
Accept-Encoding: deflate, gzip, x-gzip, identity, *;q=0
Connection: Keep-Alive, TE
TE: deflate, gzip, chunked, identity, trailers

Response
HTTP/1.1 200 OK
Cache-Control: private, no-cache, no-store, must-revalidate
Content-Encoding: gzip
Content-Language: en
Content-Type: text/html
Date: Thu, 16 Apr 2015 07:00:35 GMT
Expires: Sat, 01 Jan 2000 00:00:00 GMT
Pragma: no-cache
Server: nginx
Set-Cookie: csrftoken=84af0dfa2bd03f166b9764aa7cb5abe3; expires=Thu, 14-Apr-2016 07:00:35 GMT; Max-Age=31449600; Path=/
Set-Cookie: mid=VS9eEgAEAAEo40DmXo1fRpT5Mzp2; expires=Wed, 11-Apr-2035 07:00:35 GMT; Max-Age=630720000; Path=/
Vary: Cookie, Accept-Language, Accept-Encoding
X-Frame-Options: SAMEORIGIN
Content-Length: 8249
Connection: keep-alive

Working after cookies deleted

GET /someuserpage/ HTTP/1.1
User-Agent: Opera/9.80 (Windows NT 5.1; Edition United Kingdom Local) Presto/2.12.388 Version/12.17
Host: instagram.com
Accept: image/gif, image/jpeg, image/pjpeg, application/x-ms-application, application/vnd.ms-xpsdocument, application/xaml+xml, application/x-ms-xbap, application/x-shockwave-flash, /
Accept-Language: en
Accept-Encoding: gzip, deflate
Cookie: csrftoken=96dd728dcc2245859f866b525b6d4b46; mid=VS9fJwAEAAEI_jHXMyJgFAyIaDxB
Connection: Keep-Alive
Response
HTTP/1.1 200 OK
Cache-Control: private, no-cache, no-store, must-revalidate
Content-Encoding: gzip
Content-Language: en
Content-Type: text/html
Date: Thu, 16 Apr 2015 07:07:00 GMT
Expires: Sat, 01 Jan 2000 00:00:00 GMT
Pragma: no-cache
Server: nginx
Set-Cookie: csrftoken=96dd728dcc2245859f866b525b6d4b46; expires=Thu, 14-Apr-2016 07:07:00 GMT; Max-Age=31449600; Path=/
Vary: Cookie, Accept-Language, Accept-Encoding
X-Frame-Options: SAMEORIGIN
Content-Length: 8248
Connection: keep-alive
[/code]