If you use different units on different coordinates and if you use a different unit on the distance metric then the diagonal elements of the metric matrix can differ from 1. For example if you want to measure distances in meters, but you use inches for the x dimension and centimeters for the y dimension, then the 2D metric would be: $$\begin{bmatrix} meters^2/inch^2 & 0 \\ 0 & meters^2/centimeter^2 \end{bmatrix}$$
So in general the diagonal values can differ from 1, but it is much more sensible to use the same units for x, y and distance and in that case they will all be 1.
Now in the Minkowski 4D space-time (t,x,y,z) the metric is usually written like this:
$$\begin{bmatrix} -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$$
And in this case the -1 is for the time direction and it is significant. That cannot be changed to a +1 and is what gives significance to the speed of light - in particular light always travels a "proper" distance of 0 in the full 4D space-time. Note that a total distance of 0 is only possible if at least one of the diagonal elements has the opposite sign of the other diagonal elements. In fact, the -1 is often written as $-c^2$ which is just another indications that the unit of measurement for time differs from the units for the spatial coordinates. Again using the "same" units can change the diagonal element to -1 instead.