The act of influencing politicians in order to persuade them to care about an issue is called!

The act is called lobbying.

Lobbying is an act of attempting to influence the actions or policies of officials, mostly the legislators. Professional lobbyists are people whose business is trying to influence legislation or other government decision or action. They act on behalf of specific groups of individuals who hire them.

Professional lobbyists represent their clients in front of a government body. They work to persuade the government decision makers on behalf of their clients.

The name lobbying comes from the lobby in Willard Hotel in Washington D. C. It was used often by President Ulysses S. Grant, and it was where the political advocates gathered to approach him.