What does this mean? 'the church nearest to us is very Low and I couldn’t bear that.’?

In the Church of England, a 'low' church is one that is closer to Baptist ideas, very plain, little liturgy, not much decoration or music usually: maybe only unaccompanied singing. Some of the very lowest would have no pictures anywhere, and would not have much of a role for clergy.

In contrast, a 'high' church would have a lot of pomp and circumstance, a lot of elaborate music, probably a church choir who might wear special robes, a lot of colour and decoration, a lot of ritual and liturgy, vicars wearing special colourful vestments, etc.

A guess . . . just a guess. "High" church is a more traditional church with icons, robes, candles, incense, etc. Think Catholic or Episcopal. "Low" church is one with no robes, elaborate ceremonies, etc. Perhaps the person wanted something more in between.