The aviation industry has proposed the collective goal of achieving net-zero carbon emissions by 2050. In addition to the existing market-based methods (MBMs), the use of renewable energies, in particular, sustainable aviation fuel (SAF), could be one of the most promising means for achieving this long-term target. This paper investigates how an SAF mandate from the government can lead to heterogeneous impacts on two types of airlines, namely, full-service carriers (FSCs) and low-cost carriers (LCCs), that compete in the same markets. A game-theoretic economic model is constructed that accounts for the different service quality levels and cost structures (i.e., fuel efficiency) between FSCs and LCCs. Our analytical results suggest that the SAF mandate favors LCCs over FSCs. The share of SAF blended into fuel raises the airfares of both types of airlines while reducing the traffic and profit of FSCs. The impacts on the LCC traffic and profit depend on its fuel efficiency relative to that of FSC. When LCCs are sufficiently fuel efficient, the SAF mandate can increase their traffic and profit. The government subsidy on airline's SAF use is also analyzed, deriving the optimal subsidy levels for FSC and LCC respectively to achieve pareto-improvement in social welfare and consumer surplus. We also examine how air passengers’ environmental awareness affects the outcomes of SAF mandate implementation. Our economic model also accounts for passengers’ heterogeneous preferences in terms of service quality and price sensitivity.