Baptists can continue if they wish. Some do, some don't. Some remarry and keep pastoring. I always thought that odd.
Different people interpret the scriptures on divorce differently, but many hold that divorce is permitted if a spouse is unfaithful, or refuses to live with the Christian because he or she is a Christian
. The innocent party is not held guilty, neither is (s)he required
to divorce the unfaithful spouse, but merely has the scriptural right to, if (s)he wishes.
We do not have a doctrine of priesthood and laity, therefore a pastor cannot become lay or non-priestly, but is a pastor by reason of his appointment to that position. It's his function, not his ontology. If he is the innocent party in a divorce, there is no moral or other compelling reason why he should resign or be dismissed. However, he might possibly feel it right to resign, for the sake of the honour of the church, as pastors are required in the pastoral epistles to manage their households well, and clearly he has not achieved this, and in order to deflect malicious ill-informed gossip by outsiders or (worse) by church members.
If he is the guilty party, he should indeed resign or be dismissed, but I see no reason why he should not become a pastor again later, perhaps after some years, if there is strong enough reason to believe in his repentance and reformation. After all, the apostle Peter was reinstated, though not after the same offence.
As regards denominations, I do not know how it is in the USA, but here in Britain men become often pastors in a denomination other than their own, if the pastor and the congregation sense a oneness of mind and spirit, so that men might move without difficulty between Baptist, Congregational, independent Evangelical, or Pentecostal churches. (Many Congregational churches have adopted believers' baptism, or a man might accept a call to a pastorate with the understanding that he would not himself 'baptise' infants, but would not try to obstruct such a ceremony being performed by a visiting Congregational minister if the parents so wished.)