Is it permissible to trim and shorten the beard for the sake of da‘wah and to avoid alienating those being invited to Islam, especially if this is in an environment that may not accept a long beard?

It is not permissible to shave the beard for political reasons or for the purpose of Dawah (proselytizing/inviting to Islam). Rather, it is obligatory to let it grow long, in compliance with the command of the Messenger of Allah (peace be upon him). If Dawah becomes impossible while keeping the beard, one can move to another place. If the door to Dawah is completely shut unless the beard is shaved, and great good is expected from one's Dawah, then this becomes a matter of ijtihad (independent reasoning) based on assessing benefits and harms. The assessment of benefits should be referred to scholars. Imitating disbelievers in their lands is permissible only in dire necessity, and not in the land of Islam. The ruling on trimming the beard differs from shaving it completely. A Muslim must be proud of his religion and its rituals.