Is it permissible to abandon a pillar of prayer in order to follow the Imam, such as omitting the first tashahhud to join the Imam in his prayer?

The congregant must join the Imam in whatever state he finds him. So, if he comes to the prayer and the Imam is in a certain state, he should do what the Imam is doing. If he misses one or more rak'ahs with the Imam, he should disregard what he missed and join his Imam, then make up what he missed after the Imam’s tasleem. However, if he misses two pillars with the Imam, he should perform them and then join him, as long as he does not fear missing the subsequent rak'ah. If the Imam precedes him by one pillar, he should perform it. As for the first tashahhud, it is not a pillar but rather one of the obligations of prayer. Therefore, the latecomer should follow the Imam in it and not perform it in the third rak'ah of a four-rak'ah prayer, which would be his second rak'ah.