Display webform submitted data in profile page
If you're willing to use Webform Rules in combination with Rules, you can use the webform data (as submitted via the webform) in a custom rule (to copy those webform date to the relevant profile fields). Because you have access to all labels and all values of any field of a webform, ie:


[data:MachineFieldName-title] contains the Label of a field with machine name MachineFieldName.
[data:MachineFieldName-value] contains the Value of a field with machine name MachineFieldName


With that, you should be able to create a custom rule with:


Rules Event: After a webform has been submitted.
Rules Conditions: Check the form's id (possibly with other conditions to further refine them, eg that the user is not logged in).
Rules Action(s): Set a data value (for the appropriate profile fields, and using the values submitted via the webform).


For more details about this approach, and a prototype rule to understand the idea, refer to the answer to "How to create a node from a Webform using rules?":


the 1st attempt relates to using "Entity has field" (which doesn't work for Webform)
the 2nd attempt explains what to do in case of Webform.


PS: I'm assuming your question is about D7 ...