Yes there are certainly protestant churches that practice sanctuary.
To start with a little history, the practice of being able to 'seek sanctuary' in a church was written in Medieval English law. It was abolished in 1623, although vestiges of it existed up to the 18th Century.
In modern times few countries (none that I know of) provide for legal immunity of a fugitive just because they enter a church. However this has not prevented the practice of sanctuary, mostly for refugee claimants rather than criminals. In Canada the complete absence of any legal protection has not prevented refugees from seeking protection in churches when scheduled for deportation.
In the past 30 years, more than 50 unsuccessful refugee claimants have sought sanctuary within a Canadian church to avoid deportation, according to University of Windsor researcher Randy Lippert.
In most cases the reason for the acceptance by the church is compassion for people who face life-threatening situations.
Where a congregation’s attitude changes is “when you know that they’re going to face death or torture or imprisonment when they go home.” Canada’s refugee system is designed to shield claimants from mortal danger, but [a church member] said there are still plenty of cracks in the system, be it the bad advice of an immigration consultant, a difficulty with paperwork or even the simple nuances of speaking through a translator.
Refugee claimants have no automatic right to stay in a church.
In a 2010 York University research paper, Montreal pastor Darryl Gray said he turns away requests for sanctuary on a weekly basis, “because they are often economic refugees who can’t prove they face physical danger.”
In these cases there is no legal reason why a refugee cannot be removed from a church as from a private home. However in practice it is rarely done.
Church arrests are bad optics, particularly as sanctuary-takers are not working illegally or drawing social services, said [a law professor]. Besides, “what government wants to take on a religious community acting to uphold the value of providing refuge to strangers in need?” he said.
There are churches doing similar things in the UK.
In the US the modern Sancuary movement began in the 1980s to support Central American refugees fleeing civil war, and involved more than 500 congregations of many denominations.