Whether Taoist, Buddhist, or Catholic Christian , they never stop honouring their parents before or after death. However, one has to be careful in discerning whether they are doing ancestor worship or just praying for the dead or talking to their souls/spirits in heaven.
You noticed that Jesus took the top spot on the altar? I didn’t see any signs of joss sticks although I see there is a receptacle (or appears to be) that is used traditionally for sticking in the joss sticks. Probably converted to hold candles and matches so that the wax don’t dripped everywhere. However the arches design doesn’t look like typical Buddhist/Taoist altar design. In some land scarce countries, the cremated ashes are placed there as well.