"we should be active to shopping online" 中be active后常跟介词in,be active in doing sth.对.表示很积极主动（或对某事持积极的态度）,积极热心参加于某事
若非要用to,个人觉得也未尝不可,只是比较少见,介词to常跟不定式接动词原形,可改为 we should be active to shop online（把shop后ing去掉）
又或是把to变为towards,we should be active towards shopping online译为对网上购物持乐观积极态度.