Maven: Customize web.xml of web-app project

is there a way to have two web.xml files and select the appropriate one depending on the profile?

Yes, within each profile you can add a configuration of the maven-war-plugin and configure each to point at a different web.xml.

<profiles>
    <profile>
        <id>profile1</id>
        <build>
            <plugins>
                <plugin>
                    <groupId>org.apache.maven.plugins</groupId>
                    <artifactId>maven-war-plugin</artifactId>
                    <configuration>
                        <webXml>/path/to/webXml1</webXml>
                    </configuration>
                </plugin>
                 ...

As an alternative to having to specify the maven-war-plugin configuration in each profile, you can supply a default configuration in the main section of the POM and then just override it for specific profiles.

Or to be even simpler, in the main <build><plugins> of your POM, use a property to refer to the webXml attribute and then just change it’s value in different profiles

<properties>
    <webXmlPath>path/to/default/webXml</webXmlPath>
</properties>
<profiles>
    <profile>
        <id>profile1</id>
        <properties>
            <webXmlPath>path/to/custom/webXml</webXmlPath>
        </properties>
    </profile>
</profiles>
<build>
    <plugins>
        <plugin>
            <groupId>org.apache.maven.plugins</groupId>
            <artifactId>maven-war-plugin</artifactId>
            <configuration>
                <webXml>${webXmlPath}</webXml>
            </configuration>
        </plugin>
        ...