No. Most photographers do not avoid zoom lenses just because many have variable maximum apertures.

Zooms are widely used, and modern zoom lenses are very popular. If a changing maximum aperture were a deal-breaker for most photographers, variable-aperture zooms would not be so common. There are also constant-aperture zooms available when keeping the same maximum aperture throughout the zoom range is important.

In practice, photographers treat this like any other shooting tradeoff. If zooming changes the maximum aperture, you may need to compensate with shutter speed, ISO, lighting, or by accepting a different depth of field. Usually, getting the framing you want matters more than avoiding that adjustment.

Also, modern cameras and lenses make zooms very practical: image quality is generally strong, and current cameras handle higher ISO much better than older systems did. That reduces the downside of a lens becoming a bit slower as you zoom.

So the short answer is: no, photographers generally don’t avoid zooms for this reason—they choose between zooms and primes based on the needs of the shot, such as framing flexibility, speed, and depth of field.