Select the most appropriate option to fill in the blanks.

House and Senate Republicans are backing ________ construction of a border wall, former President Donald Trump's signature policy, while ________ large numbers of migrants ________ for asylum and reviving a ________ policy under which asylum seekers are told to remain in Mexico while their immigration case is beard.

Ingrained : (of a habit, belief, or attitude) firmly fixed or established; difficult to change.

Renowned: widely acclaimed and highly honoured: celebrated.

Ensued: happen or occur afterwards or as a result.

Renewed: to make like new. 

Considering this, only "renewed" makes sense in the first blank. 

Deeming is to come to think or judge. This fits perfectly in Blank 2 as well. Ineligible is essentially not being eligible (the migrants not being eligible). This fits in Blank 3. The policy is controversial. 

Therefore, Option D is the correct answer.