I can imagine a few ways this can be done:

Use a hidden form to perform the XHR and amp-bind to set its inputs. Then, use an action chain e.g. on="tap:AMP.setState({selection: event.targetOption}), myHiddenForm.submit. This is more flexible but requires allowing an action to wait for previous actions to complete (Support action chaining (for multiple actions in a single event) #8678).
Allow binding to the src attribute of <amp-state>, e.g. <amp-state [src]="'https://data.com/products?color=' + selectedColor + '&size=' + selectedSize">. Applying a [src] binding triggers the XHR. This is less flexible than (1) since XHR data is merged under the id of the element and a little more confusing since <amp-state> has only been used to initialize data so far (rather than dynamically fetch multiple remote data).
Add a new action AMP.fetchState(), e.g. on="select:AMP.fetchState(<url_expression>, <variable_path>)". This will cause a lot of duplication of the data URL.

(2) is consistent with our current planned solution for server-side sorting/filtering: #8368 (comment).

amp-bind: Support e-commerce XHR use case #8648

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