Lang grew up on rice but these days he shuns it because he thinks it's unhealthy.

[alpacinou]

I want to say someone ate a particular kind of food growing up. Can I say they grew up on it?

Lang grew up on rice but these days he shuns it because he thinks it's unhealthy.

Is there another way to suggest someone consumed a particular kind of food when they were growing up?

 

[Barque]

Can I say they grew up on it?

Yes.

Is there another way to suggest someone consumed a particular kind of food when they were growing up?

Various ways.

He ate [a lot of] rice growing up.
He was brought up on rice and vegetables.
The most common thing on the table when he was a child was rice.

but these days he shuns it

By the way "shun" isn't a conversational word. I daresay there are lots of native speakers who've never heard it said in real life.