No, the money your parents give you to pay for their share of household expenses is not taxable to you. You are simply acting as a conduit for the funds. The money should be used to pay for the expenses of maintaining the household, such as rent, mortgage, utilities, and groceries. You should not include this money as income on your tax return.
Sources:
Publication 525 (2023)
Publication 501 (2023)
Publication 1380
Publication 17 (2023)
Publication 225 (2023)
