some people ask their families to give money to charities ra

其实这题buy 和 to buy 都可以.
这是rather than的用法：
注意：rather than 后接不定式时,不定式可以带to,也可以不带to.
例：I decided to write rather than (to) telephone.我决定写信而不打电话.
但rather than位于句首时,则只能接不带to 的不定式.
例：Rather than allow the vegetables to go bad,he sold them at half price.他唯恐蔬菜烂掉,把它们以半价卖掉了.

不行吧

结构必须对等、一致，或者是单词、动词
to…… (give) 动词所以后面也该填(buy)动词前面是to give ,后面也应该是to buy 吧？Some people ask their families to （give money to charities） rather than（buy them gifts). 一些人要求他们的家人（捐钱给慈善机构）而不是（给他们买礼物）...