Nearly 30 people have given their support to the plans for the conversion of the 19th century former Presbyterian Church in the town, with just five objections received.
The BNP had urged people to write to Shropshire Council to object to the plans for the building, which is currently occupied by a furniture business.
The Oswestry Muslim Society has applied for planning permission to change the use of the building for prayer meetings.
Supporter Iris Gordijn wrote: "It's a very good thing that at long last Muslims will get their own religious and social centre in Oswestry.
"I fully support this application."
Another supporter, Andrew Meredith, added: "Bringing an unused building back into use can only be good thing for the town.
"The fact that it is to be used as a Muslim Centre is immaterial."