As far as I'm concerned,shopping online will be more and more popular,we should be active to shopping online,because the

"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.